QQuestion
15, 30, 60, 120, … are in G.P.
(a) Find the nth term of this G.P. in terms of n.
(b) How many terms of the above G.P. will give the sum 945?
✓Answer
Given G.P.: 15, 30, 60, 120, …
First term, a = 15
Common ratio, r = 30/15 = 2
(a) The nth term of a G.P. is:
Tₙ = arⁿ⁻¹
⇒ Tₙ = 15 × 2ⁿ⁻¹
Therefore, the nth term is 15 × 2ⁿ⁻¹.
(b) Let the required number of terms be n.
Sum of n terms of a G.P. = \frac{a(r^n-1)}{r-1}
Given that the sum is 945:
945 = \frac{15(2^n-1)}{2-1}
⇒ 945 = 15(2ⁿ − 1)
⇒ 2ⁿ − 1 = 945/15
⇒ 2ⁿ − 1 = 63
⇒ 2ⁿ = 64
⇒ 2ⁿ = 2⁶
⇒ n = 6
Therefore, 6 terms give the sum 945.
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