Question

answer it and explain

Answer 1

In a Geometric Progression, The terms are arranged in this order.

$u, uv, uv^2, uv^3, ..., uv^{n-1}$

So, in the 1st Question, the terms are

2, 6

2, 2*3

Here, u=2, and v=3

a) So, next 2 terms are

uv² and uv³

2*3² = 18

2*3³ = 54

b) The 8th Term will be

uv^7

= 2*3^7

c) The nth Term will be

$uv ^{n - 1} \\ = 2 \times {3}^{n - 1}$

In the 2nd Question

First 2 Terms are 5 and 10

i.e. 5 and 5*2

Here, u=5 and v=2

a) The common ratio is 2

b) The 10th term is

$5 \times {2}^{9}$

c) The 15th Term is

$5 \times {2}^{14}$

d) The nth Term is

$5 \times {2}^{n - 1}$