Consider the sequence where .

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Consider the sequence

2x,\;4x^{2},\;8x^{3},\;16x^{4},\ldots

where

x\ne0

. (i) Verify that the sequence forms a geometric progression. (ii) Find its common ratio. (iii) Obtain an expression for its

n

th term

a_n

. (iv) When

x=3

, calculate the value of the seventh term.