Chapter 8, Problem 3CR

To determine

The $n^{th}$ term of the given sequence.

Answer to Problem 3CR

The $n^{th}$ term of the given sequence is-

  $a_n=5n+2$

Explanation of Solution

Given: The given sequence is-

7, 12, 17, 22, 27, . . .

Concept Used: Arithmetic progression (or A.P) is a type of sequence in which the difference between any term from its succeeding term is a constant, known as the common difference, denoted by d. Thus, $a_{k+1}-a_k=d$ , k = 1, 2, 3, …, (n − 1).

Hence, any A.P. whose first term is a is of the form-

  $a,a+d,a+2d,a+3d,\mathrm{...}$

In general, the $n^{th}$ term of an A.P. is defined as-

  $a_n=a+\left(n-1\right)d$ .

Calculations: The given sequence is-

7, 12, 17, 22, 27, . . .

Here,

12 − 7 = 5,

17 − 12 = 5,

22 − 17 = 5, and so on.

This shows that the difference between two consecutive terms is a constant. Hence the given sequence is an arithmetic progression whose first term is 7 and common difference is 5.

Therefore, the $n^{th}$ term of the given sequence is-

  $a_n=7+\left(n-1\right)5$ .

  $=7+5n-5$

  $=2+5n$

Thus the required $n^{th}$ term is

  $a_n=5n+2$