Question

What is the 15th term in the sequence...pt.1​

Answer 1

this is a geometric progression

so first term a = 3

common ratio r = 12/3 or 48/12 = 4

so in GP n term is given as


`t_(n) \: = a {r}^(n - 1) \\ so \: \\ t_(1) \: = a {r}^(1 - 1) = 3 * {r}^(0) = 3 * 1 = 3 \\ t_(2) \: = a {r}^(2 - 1) = 3 * {r}^(1) = 3 * {4}^(1) = 3 * 4 = 12 \\ t_(15) \: = a {r}^(15 - 1) = 3 * {r}^(14) = 3 * {4}^(14) = 3 * 268435456 = 805306368 \\`

so answer is 805306368

Answer 2

a₁₅ = 805306368 is the 15th term of the sequence.

Explanation:

We have given a sequence :

3,12,48,192,768,...............

TO find is it geometric sequence or not:

12/3 = 4

48/12 = 4

The ratio is same so it is a geometric sequence.

common ratio= r = 4

The formula to find the n terms is given by:

aₙ = arⁿ⁻¹

First term = a = 3 , r = 4.

We have to find the 15th term of the sequence.

put n = 15 we get,

a₁₅ = 3(4)¹⁵⁻¹

a₁₅ = 3(4)¹⁴ = 3 × 268435456= 805306368.

a₁₅ = 805306368 is the 15th term of the sequence.