# Algebra

posted by .

Two questions I need help with.

Find the indicated partial sum using the information given.

1. a3=4/9, a7=9/64, S6

Determine wheater the infinite geometric series has a finite sum

2. 6+ 3+ 3/2 + 3/4 +....

3. -49 + (-7) + (- 1/7) +...

• Algebra -

1. S6 = 6/2(a+5d)
d = (A7-A3)/4
a = A3-2d

2. since |r| = 1/2 < 1, yes the sum is finits
3. same

• Algebra -

I will assume that by a3 you mean term(3)
and the terms form an geometric sequence

term(3) = ar^2 = 4/9
term(7) = ar^6 = 9/64

divide term7 by term3
r^4 = (9/64) / (4/9) = 81/256
r = ± 3/4
the in ar^2 = 4/9
a(9/16) = 4/9
a = 64/81

so Sum(6) = a(r^6 - 1)/(r-1)
= (64/81)((3/4)^6 - 1)/(3/4 - 1)
= 3367/1296
= appr 2.59799

2. term2/term1 = 1/2
term3/term2 = 1/2
since |r| < 1 , the infinite series has a finite sum

2nd one:
r = -7/-49 = 1/7
yes, so does that one

## Similar Questions

1. ### 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?
2. ### 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?
3. ### 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 …
4. ### 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 …
5. ### 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 …
6. ### 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 …
7. ### 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 …
8. ### Algebra

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

I need some help! Determine whether infinite geometric series has a finite sum. If so, find the limiting value. 112+56+28+....
10. ### 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. ---------------------------------------- …

More Similar Questions