# Geometric Series (Algebra 2)

44,288 results

Geometric Series (Algebra 2)
I need some assistance or a formula when trying to find the first term of geometric series please! I don't understand this!!!! What is the first term of a geometric series with a summation of 289, 5 terms and a common ratio of 1/2?

Algebra 2 - Geometric Series
I need help evaluating the geometric infinite series. It's got the double zero thing over the E thing. 00 E(-1/2)^ n-1 (n=1)

Convert 8.690909 . . . into a single fraction using infinite geometric series.

Algebra
1. Why cant you use the formula of the infinite geometric series on 1/81 + 1/27 + 1/9 + 1/3 + ..... 2. Using concepts of infinite geometric series, show that 0.9999 ..... = 1.

algebra
Can someone please help me with this problem? Thanks! Evaluate the infinite geometric series: 8+4+2+1+... I thought you needed to know the number of terms to evaluate, but how do you know them if it is infinite? The limit of Sn = 1 + r + r^2 + r^3 + r^4 + = 1/(1 - r) -1 < r...

Algebra II (Geometric Series)
What is the sum of the following geometric series: 1+1/4+1/16

algebra(check)
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c 3)Find the sum of ...

algebra
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c 3)Find the sum of ...

algebra
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c 3)Find the sum of ...

algebra
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c 3)Find the sum of ...

CALC II
Determine the convergence of the following series using the nth-partial sum or geometric series formula. The sum of n=1 to inifitiy 1/(9n^2+3n-2) How do I start? I'm guessing I should factor out the denominator but whats after that? It is close to a geometric series, so use ...

Algebra 2
I need steps on how to complete this please i am so confused and lost. :( Consider the infinite geometric series x e n=1 -4(1/3) n-1. In this image, the lower limit of the summation notation is "n=1". a. Write the first four terms of the series. b. Does the series diverge of ...

Pre-Calculus
Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- Q. The first term of an infinite geometric...

algebra, series
The sum of the first n terms of a series is 1-(3/4). Obtain an expression for the nth term of the series. Prove that the series is geometric, and state the values of the first term and the common ratio. Please show workings

math(geometric series)
the common ratio of the infinite geometric series whose 2nd term is 3/2 and its sum is 8?

Algebra
Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of ...

Math - Geometric Series
Find the sum of the geometric series 128 - 64 + 32 - . . . to 8 terms. a) 85 b) 225 c) 86 d) 85/2 e) not possible

Calc
We are working on finding the intervals of convergence of power series in class. Why do we not have to test for the convergence of the endpoints for geometric series? They always seem to diverge. Is this a set rule when working with the geometric series for this type of problem?

Math
1/27 + 1/9 + 1/3 + ... + 81 I know the series is geometric. d = 1/3 Multiplying each by 1/3 to get the next value do i use the sum of geometric series a(1-r^n)/ 1-r

Algebra
Is the series 72, 48, 32,... an arithmetic or geometric series. WHat is common difference or ratio

Algebra 2
Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first 4 terms of the series?

sum geometric series
what is the sum of geometric infinite series 3/2+ 9/16+ 27/128+ 81/1024=.... i know the formula is S=a/(1-r) my teacher, he usually transforms into a formula of the sum series and finds out a and r.but i don't how to do that. the pattern i saw is 3/2 + 3^2/2^4 + 3^3/2^7+ 3^4/2...

Algebra 2
Describe an infinte geometric series with a beginning vaule of 2 that converges to 10. What are the first 4 terms of the series? I know r=4/5 Now what do I do

AGL 2 (Geometric Series)
Is their a formula for finding the Sum for Geometric Series?

Calculus
If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY? Or should you do alternate series test also to say ...

Geometric Series
Evaluate the geometric Series or state that it diverges lower bound k= 1 upper bound = infinity E (sum symbol) E 5(-1/6)^(5k) I know it converges but im not sure to what

Algebra 2
Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first 4 terms of the series? Last question and my mind is fried, can someone please help me? Thanks

Math Geometric Series
Evaluate this geometric series: 7 + 14 + 28 + ... + 3584

math studies
An arithmetic series has a first term of -4 and a common difference of 1. A geometric series has a first term of 8 and a common ratio of 0.5. After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?

Math
Consider the following series: 1,2,3,4,5,10,20,40....which starts as an arithmetic series? ...but after the first five terms becomes a geometric series. Prove that any positive integer can be written as a sum of distinct numbers from the series. I know how to do the base case

math
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 A)15 B)15/2 C)-15 D)1/15 I chose A 2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1 A)25 B)80/3 C16 D)does not exist I chose A 3)Find the...

math(need 2nd opinion)
1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 A)15 B)15/2 C)-15 D)1/15 I chose A 2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1 A)25 B)80/3 C16 D)does not exist I chose A 3)Find the...

math
the last two tems in a geometric series are 1080 and 6480 and the sum ofthe series is 7775 what is the first term in the series

Math
Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of ...

algebra
Okay, I was taught that if a geometric series is infinite and it diverges then it has no limit and no sum. Looking back in my notes, I found an example of finding the value for a divergent series? Is this possible? The sum of an infinite geometric progression is infinite when ...

algebra 3-4
Find a1 in a geometric series for which Sn = 300, r = -3, and n = 4

Geometric progression
Find the sum of the geometric series 1+1/2+1/4+1/8+.....to 12th terms.

math
sorry for before it is my first time using this website and this is the real question in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62813. How many terms are in the series?

geometric series
what is the nth term equation for a geometric sequence with a1 = 36 and r = 1/3

algebra
does the infinite geometric series diverge or converge? 1/7 + 1/14 + 1/28 + 1/56 +

algebra
In a geometric series, suppose g2 = 2 and g6 = 162. What is gngn–1?

Algebra II
What is the sum of the geometric series 12 E 2(1/2)^x x=0 4 0 2 3 PLEASE HELP Urgent

trig
for the geometric series shown, state whether the series in convergent. If the series is convergent, give the sum 9 +6.3 + 4.41

Calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

calculus
Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

algebra II
Determine whether the geometric series converges or diverges. 27 + 18 + 12 + 8 + . . .

Algebra 2
5+(-5/2)+(5/4) Sn=189 Find n for the given sum if the geometric series

Algebra 2
What would happen to the sum of a geometric series if the ratio was 1?

Math
I have a couple questions about the sums of geometric series. One. So the formula for the sum is t(n)=t(1)[(r^n)-1] But if my series starts at t(0), can I change the formula to t(n)=t(0)[(r^n)-1] ? Two. If, in the series, there is a different pattern in the numerator than in ...

calc.
find the sum of the series of (-2)^n/3^n+1. This is an alternating series... what if we rewrite it as an= (1/3)* (-2/3)^(n) Divide any nth term by the n-1 term and see if you get a ratio term r. This might be a geometric series.

algebra need help
Determine whether the geometric series converges or diverges. 27 + 18 + 12 + 8 + . . .

Algebra 2
How would I find the sum of the geometric series given? 1/5 - 1/25 + 1/125

algebra 2
find a1 for given geometric series. Sn= 405, r=3, n=4 I don't know how to start the problem

math
in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 6813. How many terms are in the series

math
in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62813. How many terms are in the series

math
in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62 813. how many terms are in the series?

math
For a geometric series, S4/S8= 1/17, determine the first three terms of the series.

Algebra
Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments. Using the formula for the...

Algebra 2
Find the sum of the first six terms of the geometric series 81 -27 +9 -... how do you work it??

Series and sequences
Three numbers a,b, and c form a geometric series so that a+b+c=35 and abc=1000. Find the values of a,b,c.

Geometric Series
how do you convert a series into that beta stuff

Geometric series
Find the sum of the following series : a) 1 - 1/¡Ì2 1/2 - 1/2¡Ì2 ¡­to 20 terms.

Geometric series - Check my answer
What is the first term in a geometric series with ten terms, a common ratio of 0.5 and a sum of 511.5? I got 256 as my answer. 511.5=a1[1-(.5)^10]/1-1/2 511.5=a1(1023/1024)/1/2 511.5=a1(1023/512) ----> divide by both sides 256=a1

Geometric series
The sum of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. if the fourth term is 48, determine a(first term),r(ratio), t10, S10.

Geometric series
please help with finding the equations to these where n= 1; which means 1 is needed to find the first number in the series 1) 5/1 + 8/1 + 1/1 + 14/1 + . . . 2) 6/5 + 9/8 + 14/11 + 21/14 + . . . 3) -6/3 - 4/4 - 2/5 - 0 + . . . 4) 9/1 + 36/4 +27/9 + 144/16 + . . . 5) 20/4 + 25/5...

Math
If S1 = 0.7 and S2 = 2.1 in a geometric series, determine the sum of the first 12 terms in the series. Be sure to show all of your work.

math C2 sequences and series
The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and common ratio r. a)Given that d is not equal ...

trig
for the geometric series shown, state whether the series in convergent. If the Series is convergent give its sum 9+6.3 +4.41 +... a tutor helped me earlier but how is the sum 0.7

Algebra 2
What is the first term of a geometric series with a summation of 800, 4 terms and a common ratio of 3?

Algebra 2
What is the first term of a geometric series with a summation of 800, 4 terms and a common ratio of 3?

Math
which is the easies,t Arithmetic Series or a Geometric Series? and why?

Math
Does the following infinite geometric series diverge or converge? Explain. 1/5 + 1/25 + 1/125 + 1/625 A) It diverges; it has a sum. B) It converges; it has a sum. C) It diverges; it does not have a sum. D) It converges; it does not have a sum. I am pretty sure that it is ...

Algebra
Find the sum of the infinite geometric series given by ∑_(k=1)^∞〖(2/9)^k〗

Algebra 2
What is the sum of a geometric series with first term a1= 2, a common ratio r of 2 and the number of terms, n, equal to 4.

math
The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

Algebra 2
What is the sum of the geometric series 10 E 6(2)^n n=1 I'm a little lost as to what I should do here. Could someone please clarify how this one is done?

Sequence and series
Do you know the difference between a sequence and a series? Graph the terms of an arithmetic series. Remember the domain is the set of natural numbers, not the set of real numbers. What type function do you see? Graph the terms of a geometric series. Remember the domain is the...

Calc II
Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, give an approximation of its sum, ...

Calculus
If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1

mathematics
the 1st term of arithmetic series is 2 .the 1st ,3rd and 11th terms are the first the terms of a geometric series. find the 6 terms of the arithemetic series

math
The 65th therm in a geometric sequence is 8000, and the 69th term is 500, find the 64th term using the geometric series sum formula

algebra
1)Find the sixth term of the geometric sequence for which a1=5 and r=3 a.1215 b.3645 c.9375 d.23 answer=a 2)Write an equation for the nth term of the geometric sequence -12,4,-4/3,... a.an=-12(1/3)n-1 b.an=12(-1/3)n-1 c.an=-12(-1/3)-n+1 d.an=-12(-1/3)n-1 answer=d 3)Find four ...

algebra
1)Find the sixth term of the geometric sequence for which a1=5 and r=3 a.1215 b.3645 c.9375 d.23 answer=a 2)Write an equation for the nth term of the geometric sequence -12,4,-4/3,... a.an=-12(1/3)n-1 b.an=12(-1/3)n-1 c.an=-12(-1/3)-n+1 d.an=-12(-1/3)n-1 answer=d 3)Find four ...

algebra
1)Find the sixth term of the geometric sequence for which a1=5 and r=3 a.1215 b.3645 c.9375 d.23 answer=a 2)Write an equation for the nth term of the geometric sequence -12,4,-4/3,... a.an=-12(1/3)n-1 b.an=12(-1/3)n-1 c.an=-12(-1/3)-n+1 d.an=-12(-1/3)n-1 answer=d 3)Find four ...

algebra(check)
1)Find the sixth term of the geometric sequence for which a1=5 and r=3 a.1215 b.3645 c.9375 d.23 answer=a 2)Write an equation for the nth term of the geometric sequence -12,4,-4/3,... a.an=-12(1/3)n-1 b.an=12(-1/3)n-1 c.an=-12(-1/3)-n+1 d.an=-12(-1/3)n-1 answer=d 3)Find four ...

College Algebra
Find the sum of the infinite geometric series given by ∑_(k=1)^∞▒〖(2/9)^k.〗

math30
The sum of the first 10 terms of the geometric sequence -4, 6, -9,..., to the nearest tenth, is; The answer is: For the geometric series a=-4, r=-1.5 or -3/2, n=10. Sn= a(r^n - 1)/r - 1 S10= -4((-1.5)^10 - 1)/-1.5 - 1 S10= 90.7 My question is from where they got r=-1.5 or -3/2...

Calculus - - Reiny
If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1

14, 8, -16, 32... Arithmatic. 64, 128, 256 geometric, -64, 128, -256 geometric, -48, 64, -80*** the sequence is neither geometric nor arithmatic 81, 27, 9, 3.. aruthmatic , 0,-3,-6 geometric, 0,-3,-6 geometric, 1, 1/3, 1/9

Math
1. Find the 11th term of the geometric sequence 64, -32, 16, -8, … . 2. Find the 1st term of a geometric sequence with a 10th term -1024 and r = -2. 3. Find the sum of each infinite geometric series, if possible. a. 10 + 2 + 2/5 + ..... b. 1.2 – 2.4 + 4.8 – 9.6 + ..... c...

Algebra 2 (Geometric Series)
Write (2x+3y)^3 in expanded form I need a little help as far as how I would begin working this problem out.

Algebra
I need some help! Determine whether infinite geometric series has a finite sum. If so, find the limiting value. 112+56+28+....

Algebra
I need some help! Determine whether infinite geometric series has a finite sum. If so, find the limiting value. 112+56+28+....

maths
The first term of a geometric sequence is 31(1/4),the last term is 2 and the sum of the associated series is 50(3/4).what is the common ratio and how many terms are there in the series?

calculus
determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

Maths - Geometric Progression
The second term of a GP is 1/2 and the sum ti infinity of the series is 4. Find the first term and and the common ratio of the series.

calculus
Another problem: determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

math
For the geometric series 50+48+... a. 867.373 is the approximate value of a partial sum of the series. How many terms were added to get this number? b. To what number does the serveries converge?

maths and science
The first term of a geometric sequence is 125÷4,the last term is 2, and the sum of the associated series is 203÷4. What is the common ratio and how many terms are there in the series?

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