Question

Consider an a.P. With first term a and the common difference d. Let denote the sum of its first k terms. If is independent of x, the

Answer 1

Answer:

We are Given that

Arithmetic propagation have first term equal to a

common difference = d

NOW

Second term of A.P = a + d

And

3rd term = a + d + d = a + 2d = a + (3 -1) d

And so on

kth term =  a + (K -1) d

We already know that

Sum of nth terms of A.P = Sn = (n / 2)(a1 + an) = (n / 2)(a1 + a1 + (n-1)d)

In our case

a1 = a

and

an = ak

so

Sum of kth terms of A.P = Sn = (k / 2)(a + ak) = (k / 2)(a + a+ (k-1)d)

                                           Sn = (k / 2)(2a + (k-1)d)

We see that Sn is depended on

value of k,

value of a

and

value of d.