Given the geometric sequence that starts

Question

7, 9, . . .
(a) Find the 7th term of the sequence. (Given that 7 is the first term.)
(b) Decide whether you can find the sum of all the terms of your sequence. If you can, find
that sum, otherwise, find the sum of the first 13 terms of the sequence.

Answer 1

r = 9/7
(a) a_9 = ar^8 = 7(9/7)^8
since r > 1 the infinite sum diverges.
S13 = (r^13 - 1)/(r-1) = ((9/7)^13 - 1)/(9/7 - 1) ≈ 88.32

Answer 2

the ratio (of consecutive terms) is ... 9/7

(a) the 7th term is ... 7 * (9/7)^6

(b) the ratio is not <1 , so the sequence does not converge
... the sum of the entire sequence is infinite

the sum of the 1st 13 terms ... (7 * {1 - [(9/7)^13]}) / [1 - (9/7)]

Answer 3

rats - forgot the a.
S13 = a(r^13 - 1)/(r-1) = 7*((9/7)^13 - 1)/(9/7 - 1) ≈ 618.24