Answer to Question #297192 in Chemistry for Victoria

Question

Which term of the sequence 3, 12, 48,... is equal to 196 608?

Is it 12th, or, 10th, or 11th, or 9th.

Answer 1

Solution:

3, 12, 48, ... ,196608

Clearly, the given sequence is an G.P. (Geometric Progression).

The given G.P. has first term a = 3 and the common ratio r = 4.

n^th term of a G.P.:

a_n = a × rⁿ⁻¹

Let the n^th term be 196608 (a_n).

Then,

196608 = 3 × 4ⁿ⁻¹

65536 = 4ⁿ⁻¹

4⁸ = 4ⁿ⁻¹

8 = n − 1

n = 9

Answer: It is 9^th term.