Question

If each term of an A.P is increased by constant k then the nth term of the resulting A.P is ?

Answer 1

The nth  term of the resulting A.P is (a + k) + (n -1)d.

Step-by-step explanation:

We are given that each term of an A.P is increased by constant k.

Firstly, let the original arithmetic progression be;

a, (a + d), (a + 2d), (a + 3d),..........., and so on.

Here, first term = a

Common difference = 2nd term - 1st term

                                  = a + d - a = d

Now, it is said that each term of an A.P is increased by constant k, so the resulting A.P. series will be;

(a + k), (a + k + d), (a + k + 2d), (a + k + 3d),.........., and so on.

Here, First term = (a + k)

common difference = (a + k + d) - (a + k)

                                 = a + k + d - a - k = d

As we know that the nth term of an A.P. is given by the following formula;

$a_n = a + (n - 1)d$

So, nth term of the resulting A.P is = (a + k) + (n -1)d                                        

Answer 2

Step-by-step explanation:

The nth term of the resulting A.P is (a + k) + (n -1)d.

Step-by-step explanation:

We are given that each term of an A.P is increased by constant k.

Firstly, let the original arithmetic progression be;

a, (a + d), (a + 2d), (a + 3d),..........., and so on.

Here, first term = a

Common difference = 2nd term - 1st term

= a + d - a = d

Now, it is said that each term of an A.P is increased by constant k, so the resulting A.P. series will be;

(a + k), (a + k + d), (a + k + 2d), (a + k + 3d),.........., and so on.

Here, First term = (a + k)

common difference = (a + k + d) - (a + k)

= a + k + d - a - k = d

As we know that the nth term of an A.P. is given by the following formula;

a_n = a + (n - 1)da

n

=a+(n−1)d

So, nth term of the resulting A.P is = (a + k) + (n -1)d

HOPE IT HELPS