In an AP the first term is 2 and the sum of the first five terms is one fourth of the sum of the next five terms. Show that the 20th term is 112.
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math
5. In a geometric sequence, the sum of the first five terms is 44 and the sum of the next five terms is 11/8. Find the common ratio and first term of the series.

math
The sum of the first 20 terms of an arithmetic series is identical to the sum of the first 22 terms. If the common difference is 2, find the first term.

maths
The thirteenth term of an arithmetic progrssion os 27 and the seventh term is three timees the second term. tind the first term,common difference and the sum of the first ten terms

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.

maths
the sum of the first two terms of a GP is 28,but the sum of the third and fourth terms is 252.find the second term of the gp if the seventh term is 5103. please help.

Math
A g.p has 8 terms.If the sum of first 4 terms is 45 and the sum of the last 4 term is 720, find the common ratio and the first term.

Maths
1) In the arithmetic progression, the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from the 8th to the 20th term inclusive. 2) Find the least number of terms of the AP, 1+3+5...that are

Mathematics
The sum of the 1st and 2nd terms of an AP is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms

Math
The third term of a geometric progression of positive terms is 18 and the fifth term is 162 Find the common ration and the first term? Write an expression for the Nth term of the progression? Find the sum of the first 8 terms of the progression??

algebra
The fifth term of an A.P exceeds twice the second term by 1.The tenth term exceeds twice the fourth term by 3. Find:1.the first term. 2.the common difference. 3.the sum of first twenty five terms.

Additional Mathematics
The eighth term of a geometric progression is 32 and the fourth term is 2. Find the first term and the positive value of the common ratio b) find the sum to infinity of a geometric progression whose first term is 5 and second term is 4 c) The nth term of

maths
A) In an arithmetic progression the sum of the first ten terms is 50 and the fifth term is three times the second term (1) Calculate the first term (2)Calculate the sum of the 20 terms

Math3c
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.

maths
In an arithmatic sequence, sum of 9 terms is 279 and sum of 20 terms is 1280. Find 5th term ? Find 16th term ? Write the sequence.

mathematics
In a geometric progression with terms, the sum of the first and last term is 66 and the product of the second and second last term is 128. Given that the sum of all the terms of this geometric progression is 126, find the number of terms and possible

Further mathematics
An exponential sequence of positive terms and a linear sequence have the same first term.the sum of their first terms is 3 the sum of their second terms is 3/2,and the sum of their third terms is 6.find their fifth terms.

arithmetic
in an arithmetic progression the 13th term is 27 and the 7th term is three times the second term find;the common difference,the first term and the sum of the first ten terms

Maths
The 14th term of an A.P is 96,while 25th term is 173 find the ,19th term,sum of 13th and 56th terms,product of 6th and 13th terms.

Math *URGENT
Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine the geometric mean of 8

Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is 4/3 less than the sum of

Math
1) If the sum of the first n terms of a series is Sn where Sn=2n²n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP the 6th term is half the

Math
The sum of the 4th and 6th terms of an AP is 42. The sum of the 3rd and the 9th term of progression is 52, find the first term and the common difference of the sum of the 1st, 10th terms of the progression

maths
the sum of first 8 terms of an arithmetic progression is 156.the ratio of its 12th term to its 68th term is 1:5.calculate the first term and the fifteenth term. please help this questions please.

Mathematics
The sum of the first 10 terms of an Ap is 145 and the sum of its fourth and ninth is 5 times the third term determine the first term and the constant difference

A.P
The sum of 16th term is 240,the sum of the next four terms is 220.Find the first term and the common difference.

Math
The sum of the first 10 terms of an arithmetic series is 145 and the sum of its fourth and ninth term is five times the third term. Determine the first term and constant difference

math
The second term of a GP is 81 and the fourth term is 9. Find, (i) the common ratio, (ii) the sum of the first terms, (iii) the sum to infinity.

mathematics
sum of the first 2 terms of an increasing GP is 20. Sum of the second term and third term of the same GP is 30. Determine the common ratio.

Maths
The sum of the first six term of an Ap is 72 and the second term is seven times th fifth term. Find the first term and common diff. And sum of the first ten terms.

Math
The sixth term of an arithmetic progression is 265 and the sum of the first 5 terms is 1445. Find the minimum value of n so that the sum of the first n terms is negative.

Community technical college
Given that 1st term of an A.P is 7 and it's 10th term is twice the second term,calculate the (a) 19th term (b)sum of 28 terms (c) difference between 9th and 6th terms

maths
the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

Mathematics
In an arithmetic sequence the sum of the first ten terms is 400 and the sum of next ten terms is 1000. Find The common difference The first term The first three terms of arithmetic sequence are also 2x, x+4 and 2x7. Verify that when x = 8 the term form a

Math
The forth term of an A.P is four times the first term. The sixth term is sixty, find the sum of 30 terms, common difference, and the first term.

Mathematics
If the sum of the first two terms of a G.P is 3 and the sum of the second and third term is 6, find the sum of the first term and common ratio.

Precalculus
The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers is constant. So if

mathematics
the 10th term of an arithmetic sequence is equal to the sum of 40 and 5th term.If the 15th term is 127 what is its common difference?what is its first term?what is the sum of the first 30 terms.

math
The no of terms in an AP is 40 and the last is 54,given that the sum of the 15 terms added to the sum of the first 30 terms is zero.calculate(1)the first term and common difference.(2)sum of progression

maths
An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference. pl give me the answer.

Maths
The sum of the last three terms of a G.P having n terms is 1024 times the sum of the first three terms of the progression. If the third term is 5, find the last term.

arithmetic
In an AP the first term is 2 and the sum of the first five terms is one fourth of the sum of the next five terms. Show that the 20th term is 112.

maths
The thirteenth term of an arithmetic progrssion os 27 and the seventh term is three timees the second term. tind the first term,common difference and the sum of the first ten terms

Mathematics
if the sum of the 3rd and 8th terms of an ap is 7 and the sum of 7th and 14th term is 3 ,find of 10th term

Maths progression
In an AP whose first term is 2,the sum of first five term is one fourth the sum of the next five terms.show that T20=112. Find S20.

arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

maths
1) The first term of arithmetic progression is 20 and the sum of it's term is 250. find it's last term if the number of it's terms is 10 2) Find the fifth term from the arithmetic progression 12, 9, 6 hence find the sum of it's first fifty terms. 3)

Mathematics
Given that the first term of an AP is 7and it's 10th term is twice the second term.calculate the sum of it's 28th terms and the difference between the 9th and 6th term.

maths
The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is 80 . Find the terms of A.P.

math
The third term of a G.P is 24 and the sum of the first two terms is 288. If all the terms are positive,find a)the first term and the common ratio b)the sum of all the terms from 4th term to the 8th term

math
The su吗the sum of the 1st twentyone of linear sequence is 28, and sum of the first twenty eight terms is 21.find (a) the term of the sequence that is equal to 0. (b) the sum of the terms preceding the term 0

maths
in GP the product of the Second term and fifth term is double the firth term. find the first term if the sum is first terms is 80 show that r^3+r^2+r+1=40 b. hence find the value of r c.show that the value of the sum of the nth term is 3^n1

math
An arithmetic progression has 2 as its first term. find its common difference if the sum of 33 terms is equal to six times the sum of 13 terms

math
The sum of 18 terms of an A.P is 504 while the sum of its 9 terms is 126.Find the sum of its 30 term

Math
Given that the 7th term of AP is 3 greater than the 5th term,the sum of the 10th term and 3th term is 45, calculate,20th term,8 term and the sum of the first five terms?.

arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

Mathematics
The 25 term of an Arithmetic Progression is 7 1/2 and the sum of the first 23 terms is 98 1/2. Find the i. 1st term ii. common difference iii. sum of the first 30 terms

Mathematics
If the sixth term of an arithmetic progression (A.P) is 37 and the sum of the six term is 147, find the first term, common difference, sum of the first fifteen terms

Math
A geometric sequence , the fifth term is four times the third terms, the second term is 4. If r

Math(arithmetic & Geometric Series)
1)The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is 8. Find the first term and the common difference? 2)If in a geometric sequence the sum of the second and the third is 20 and the sum of the fourth and fifth is 320, find the common

Sms 1202
The 14th term of an A.P is 864,while 25th term is 1557 find the ,19th term,sum of 13th and 56th terms,product of 6th and 13th terms.

Math
The sum of the first seventeen terms of an arithmetic series is 493 The third term is 11. Find the first term and the seventeenth term. The nth term is 3*n + 2

Advanced Algebra
The arithmetic progression has first term 4 and last term 34. If the sum of its terms is 247, find the number of terms and their common difference.

Mathematics
If the sum of 3th and 8th terms of an A.p is 7 and the sum of 7th and 14th term is 3,find the 10th term .

Math:A.P.
The 1st,3rd and 9th terms of an A.P are the three terms of a G.P.if the 7th term of the A.P is 19.calculate the 20th term of the A.P and the sum of the first 12terms of the G.P(LEAVING YOUR ANSWER IN INDEX FORM)

Maths
The Ratio Of The 2nd Term To The 7th Term Of An A.P Is 1:3 And Their Sum Is 20.Calculate The Sum Of The 1st Terms Of The G.P

Mathematics
The sum of the second and third term is6 and the sum of the third and fourth is 12.Find, _The common ratio _The sum of number of consecutive terms of an arithmetic progression is 19,1/2.The first term is 16,1/2 and the common difference is 3.Find the

Geometric
1) The sum of last three terms of GP having n terms is 1024 time the sume of first 3 terms of GP. If 3rd term is 5. Find the last term. 2) The sum of the first eight terms of a GP is five times the sum of the first four terms. Find the common ratio.

Maths
The 2nd, 5th, and 14th term Of an AP are consecutive terms of a GP. Given that the sum of the three terms of the AP is 9, find the A, first term and the common difference of the AP. B common ratio of the GP C sum of the first three terms of the GP

algebra 2
An arithmetic progression has 5 terms that have a sum of 200. The sum of the last three terms added to 6 times the sum of the first two terms equals zero. What is the first term?

Math
An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference.

math
The first and seventh terms of a sequence are both 8. Starting with the third term, each term is the sum of the two previous terms. What is the fifth term?

Math (sequence)
A sequence is generated where is term is equal to the sum of to preceding terms. If the first 2 terms are 1 and 2, what is the fifth term? Please explain the logic.

algebra
If an A.p. Fifth term exceeds twice second term by 1. The tenth term xeceeds twice fourth term by 3 * find first term and common difference * find sum of first twentyfive terms.

mathG.P and A.P
A) which down the first G.P 5+10+20+.....to exceed 400000? B) in an A.P,the sum of the first five term is 30, and the third term is equal to the sum of the first two. Write the first five terms of the progression.

math
the sum of 8th terms of an AP is 549 while the common difference is 3. find the 56th term and the sum of it's 32 terms

Maths
A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?

Math....Please help I have a deadline for tonight!
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) 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.

math
1) If the sum of the first n terms of a series is Sn where Sn=2n²n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP the 6th term is half the

Arithmatic Progression
The sum of the first 5 terms of an AP is 40 and the 7th term is equal to 4 times the second term, find the first term (a), common difference (d) and the sum of the second five terms.

Math
In GP the Eleventh term is 128 times the fourth term,and the sum of second term and third term is 6. Find: 1) Common ratio. 2)Sum of the first five terms

Math
Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution

maths
The sum of the first two terms of a gp is 28, but the sum of the 3rd and 4th terms is 252. find the 2nd term of the GP if the 7th term is 5103.

Further mathematics
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms

Further maths
The first thirdd and ninth terms of am AP are the first three terms of a GP. If the seventh term of AP is 14, calculate (a) the 20th term (b) the sum of the first twelve terms of the GP

Mathematics
The sum of the first 20 terms of the linear sequence is 28 and the sum of the first twenty eight term is 21 find which is 0 and also the sum of the term preceding it

algebra 2 help please/check
The first 3 terms in a geometric sequence are 1.1, 1.65, and 2.475. Part A: What is the sum of the first 6 terms of the sequence? Show your work. Part B: How does the sum of the seriesy differ from the 6th term? Explain. Part C: If the nth term in this

algebra 2
The first 3 terms in a geometric sequence are 1.1, 1.65, and 2.475. Part A: What is the sum of the first 6 terms of the sequence? Show your work. Part B: How does the sum of the seriesy differ from the 6th term? Explain. Part C: If the nth term in this

Algebra II
The first 3 terms in a geometric sequence are 1.1, 1.65, and 2.475. Part A: What is the sum of the first 6 terms of the sequence? Show your work. Part B: How does the sum of the series differ from the 6th term? Explain. Part C: If the nth term in this

math
The sum of first 13th term as G.P. Is 21 and the sum of 21th term in 13. find the sum of first 34th terms.

math
if the 7th term of an a.p is twice the third term and the sum of the first four terms is16 and the last and the last term is 72, find the number of the terms

math
The sum of the first 10 terms of an arithmetic series is 145 and the sum of its fourth and ninth term is five times the third the..determine the first term and constant difference

math ( sequence )
A sequence is generated in which each term is equal to the sum of the two preceding terms, If the first two terms are 1 and 3, what is the sixt term? a. 11 b. 14 c. 18 d. 22 e. 29 please answer and explain

arithmetic
an arithmetic progression has 20 terms. the sum of all the even terms is 350. given that the first term is 5, find the common difference and the eleventh term.

maths
The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is 80 . Find the terms of A.P.

prasanna high school
Maths quection inam A.P. The sum of first six terms is 6an the product of second term and fifth term is 80. Find the terms of A.P.

Math (11)
The sum of the first 16 terms of an arithmetic sequence is 23 times the sum of the first 4 terms. Find the 10th term of the sequence if the first term is 2

mathematics
In an ap d sum of d 1st ten terms is 50 nd d fifth term is 3times the 2nd term.find the first nd d sum of d 1st 20 terms

Maths
progreIn a certain Ap the sum of the first and fifth term is 6 more than the 3rd term.Show that the sum of the first 10 terms of thession is 160.

mathematics
The sum of the first 2 terms of a G.P is 28,but the sum of the third and fourth is 252.Find the second term of the G.P if the seventh term is 5103

algbebra
The fifth term of an A.p. Exceeds the second term by 1.The tenth term exceeds twice the fourth term by 3 * find first term and common difference * sum of first twentyfive terms.