Question

The general term of a sequence is give by a_n = −4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Answer 1

In the given problem, we need to find that the given sequence is an A.P or not and then find its 15^th term and the common difference.

Here,

Now, to find that it is an A.P or not, we will find its few terms by substituting

So,

Substituting n = 1, we get

Substituting n = 2, we get

Substituting n = 3, we get

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

We find the common difference (d)

Thus,

Also,

Since

Hence, the given sequence is an A.P and its common difference is

Now, to find its 15^th using the formula

First term (a) = 11

n = 15

Common difference (d) = −4

Substituting the above values in the formula

Therefore,