Question

Write the sequence with nth term:

a_n = 6 – n

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 = 6 − n

So,

Substituting n = 1, we get

`a_1 = 6 -1`

`a_1 = 5`

Substituting n = 2, we get

`a_2 = 6 - 2`

`a_2 = 4`

Substituting n = 3, we get

`a_3 = 6 - 3`

`a_3 = 3`

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 = 4 - 5`

= -1

Also

`a_3 - a_2 = 3 - 4`

= -1

Since `a_2 - a_1 = a_3 - a_2`

Hence, the given sequence is an A.P.