Chapter 8, Problem 4CR

To determine

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

Answer to Problem 4CR

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

  $a_n=52-2n$

Explanation of Solution

Given: The given sequence is-

50, 48, 46, 44, 42 . . .

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-

50, 48, 46, 44, 42 . . .

Here,

48 − 50 = $-2$ ,

46 − 48 = $-2$ ,

44 − 46 = $-2$ , 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 50 and common difference is $-2$ .

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

  $a_n=50+\left(n-1\right)(-2)$ .

  $=50-2n+2$

  $=52-2n$

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

  $a_n=52-2n$