Question

The algebraic forms of some sequence are given below. Check whether each of them is an arithmetic sequence or not; also find out the first term and the common difference of the arithmetic sequence

(i) x_n = 4 − 3n

(ii) x_n = n² + 2

(iii)

(iv)

(v) x_n = (n + 1)² − (n − 1)²

Answer 1

(i)

We know that every sequence of the form is an arithmetic sequence.

Given sequence is , which can also be written as

On comparing with , we get that the given sequence is an arithmetic sequence.

Common difference = a = −3

First term = a + b = −3 + 4 = 1

(ii)

We know that every sequence of the form is an arithmetic sequence.

Given sequence is

On comparing with , we get that the given sequence is not an arithmetic sequence.

(iii)

We know that every sequence of the form is an arithmetic sequence.

Given sequence is , which can also be written as

On comparing with , we get that the given sequence is an arithmetic sequence.

Common difference = a =

First term = a + b =

(iv)

We know that every sequence of the form is an arithmetic sequence.

Given sequence is , which can also be written as

On comparing with , we get that the given sequence is not an arithmetic sequence.

(v)

We know that every sequence of the form is an arithmetic sequence.

Given sequence is

Now, this sequence can also be written as

On comparing with , we get that the given sequence is an arithmetic sequence.

Common difference = a = 4

First term = a + b = 4 + 0 = 4