Question

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) +...

Answer 1

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

Answer 2

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