Question

15, 30, 60, 120.... are in G.P. (Geometric Progression):

1. Find the n^th term of this G.P. in terms of n.
2. How many terms of the above G.P. will give the sum 945?

Answer 1

a. Given, G.P. is 15, 30, 60, 120....

Here, a = 15

Common ratio (r) = `30/15` = 2

Then a_n = ar^{n – 1}

= 15(2)^{n – 1}

b. Sum of n terms,

`S_n = (a(r^n - 1))/(r - 1)`   ...(∵ r > 1)

`\implies 945 = 15((2^n - 1))/(2 - 1)`

`\implies 945/15 = 2^n - 1`

`\implies` 63 = 2ⁿ – 1

`\implies` 63 + 1 = 2ⁿ

`\implies` 64 = 2ⁿ

`\implies` 2ⁿ = 64

`\implies` 2ⁿ = 2⁶

∴ n = 6

Hence, the number of terms needed is 6.