Question

Find the AP whose 3rd term is -13 and 6th term is 2.

Answer 1

Let a be the first term and d be the common difference.

Now, a3=-13

=> a + 2d = -13 ---------(1)

now, a6 = 2

=> a + 5d = 2 -----------(2)

Subtracting (1) from (2) we get

5d-2d = 2+13

3d = 15

d = 5

Now, from equation (1) we get

a = -13 - 2x5 = -23

The required A.P is given by

a, a+d, a+2d, ...........

So, A.P is -23, -18, -13, -8, -3, 2,......