Question

find the smallest number of terms of the geometric progression 2,3,9/2, .... which must be taken so that the sum exceeds 60

Answer 1

7

Explanation:

common ratio: 3/2=1.5

Sum of first nth term: S = a₁ * (1-rⁿ) / (1-r)

60 = 2 * (1 - 1.5ⁿ) / (1 - 1.5)

1.5ⁿ = 16

n = 6.8

s>60 n=7

check: S₇ = 2 * (1-1.5⁷) / (1-1.5) = 64.34

S₆ = 2 * (1-1.5⁶) / (1-1.5) = 41.56