Question

Write the sequence with nth term a_n = 5 + 2n

Answer 1

In the given problem, we are given the sequence with the n^th term `(a_n)`.

We need to show that these sequences form an A.P

a_n = 5 + 2n

Now, to show that it is an A.P, we will find its few terms by substituting  n =1, 2, 3

So

Substituting n = 1, we get

`a_1 = 5 + 2(1)`

`a_1 = 7`

Substituting n = 2, we get

`a_2 = 5 + 2(2)`

`a_2 = 9`

Substituting n = 3, we get

`a_3 = 5 + 2(3)`

`a_3 = 11`

Further, for the given to sequence to be an A.P,

Common difference (d)  = `a_2 - a_1 = a_3 - a_2`

Here

`a_2 - a_1 = 9 - 7`

= 2

Also

`a_3 - a_2 = 11 - 9`

= 2

Since `a_2 - a_1 = a_3 - a_2`

Hence, the given sequence is an A.P