Question

7. The sum of the first two terms of a geometric sequence is 36 and the product of the first and third terms is 9 times the second term. Find the sum of the first 8 terms.​

Answer 1

40.49

Explanation:

First term: a n term: aₙ common ratio: r sum of first n term: sₙ

a + (ar) = a(r+1) = 36

a * ar² = 9 * ar .... divide ar both side

ar = 9 ... 2nd term

a + (ar) = a + 9 = 36

a = 27 ... first term

r = 9/27 = 1/3

sₙ = a (1 - rⁿ) / (1-r) n=8

s₈ = 27 * (1 - 1/3⁸) / (1 - 1/3)

= 27 * (1 - 1/6561) / 2/3

= 27 * (6560/6561) / 2/3

= 27 * 3280/2187

= 3280/81

= 40.49