Question

If the sum of first terms of an ap is 4n-n squar , find 3rd and the 10th term

Answer 1

Refer the answer......

Answer 2

HI.

Question,

✏ If the sun of the first n terms of an AP is
4n - n² . Find 3rd and 10th term.

Solution,

➡ Given : Sn = 4n - n²

==> Taking n = 1,

we have,

Sn = 4n - n²

==> S1 = 4(1) - (1)²

==> S1 = 4 - 1

==> S1 = 3

Since,

S1 = a1

==> a1 = 3

Thus, first term of Given Arithmetic progression is 3.

again,

taking n = 2

we have,

Sn = 4n - n²

==> S2 = 4(2) - (2)²

==> S2 = 8 - 4

==> S2 = 4

Now,

a2 = S2 - S1

==> a2 = 4 - 3

==> a2 = 1

Let common difference be d.

==> d = a2 - a1

==> d = 1 - 3

==> d = -2

Now,

We know,

a3 = a1 + 2d

==> a3 = 3 + 2(-2)

==> a3 = 3 - 4 = -1

and,

10th term,

a10 = a + 9d

==> a10 = 3 + 9(-2)

==> a10 = 3 - 18

==> a10 = -15

Thus,

a3 = -1 and a10 = -15

Hope it helps you