Chapter 3, Problem 20PT

To determine

To find: $n^{th}$ term in the sequence.

Answer to Problem 20PT

Given sequence is not Arithmetic.

Explanation of Solution

Given information:

  $0.75,1.5,3,6,12,\mathrm{.....}$

Concept:

An Arithmetic sequence adds or subtracts a fixed amount (common difference) to get the next term in the sequence.

We know $n^{th}$ term of Arithmetic progression is

  $a_n=a+\left(n-1\right)d$

Where

  $a$ = First term

  $d$ = Common difference

Calculation:

Given series is

  $0.75,1.5,3,6,12,\mathrm{.....}$

Difference between first two terms = $1.5-0.75=0.75$

Difference between second and third terms = $3-1.5=1.5$

Difference between third and fourth terms = $6-3=3$

As difference of any two consecutive terms is not same.

So, given sequence is not Arithmetic.