Question

Write the sequence with nth term:

(i) a_n = 3 + 4n

(ii) a_n = 5 + 2n

(iii) a_n = 6 − n

(iv) a_n = 9 − 5n

Show that all of the above sequences form A.P.

Answer 1

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

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

(i)

Now, to show that it is an A.P, we will first 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,

Common difference (d)

Here,

Also,

Since

Hence, the given sequence is an A.P

(ii)

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

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

Common difference (d)

Here,

Also,

Since

Hence, the given sequence is an A.P

(iii)

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

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

Common difference (d)

Here,

Also,

Since

Hence, the given sequence is an A.P

(iv)

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

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

Common difference (d)

Here,

Also,

Since

Hence, the given sequence is an A.P.