Posted by **Becca** on Monday, April 8, 2013 at 10:38pm.

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 -
**Steve**, Tuesday, April 9, 2013 at 12:16am
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 -
**Reiny**, Tuesday, April 9, 2013 at 12:22am
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

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