Asked by jenny
Given the geometric sequence that starts
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.
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.
Answers
Answered by
oobleck
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
(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
Answered by
R_scott
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)]
(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)]
Answered by
oobleck
rats - forgot the a.
S13 = a(r^13 - 1)/(r-1) = 7*((9/7)^13 - 1)/(9/7 - 1) ≈ 618.24
S13 = a(r^13 - 1)/(r-1) = 7*((9/7)^13 - 1)/(9/7 - 1) ≈ 618.24
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