Question

Show that the sequence defined by a_n = 5n −7 is an A.P, find its common difference.

Answer 1

In the given problem, we need to show that the given sequence is an A.P and then find its common difference.

Here,

Now, to show that it is an A.P, we will find its few terms by substituting

So,

Substituting n = 1, we get

Substituting n = 2, we get

Substituting n = 3, we get

Substituting n = 4, we get

Substituting n = 5, we get

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

We find the common difference (d)

d

Thus,

Also,

Since

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