IF A.P(arithmetic progression) has 13 terms whose sum is 143.

Question

the third term is 5 , then first term is =?

Answer 1

The sum of first n terms in A.P : .

From the given data :

n = 13, s_n = 143 and the third term = a + 2d = 5.

143 = (13/2)[2a + (13 - 1)d]

286 = 13(2a + 12d)

22 = 2a + 12d

a + 6d = 11  --------------> (1)

a + 2d = 5    --------------> (2)

Subtract (2) from (1).

a + 6d = 11

a + 2d = 5

( - )__________

4d = 6

d = 6/4 = 3/2.

Substitute the value of d = 3/2 in equation (2).

a = 5 - 2d

= 5 - 2(3/2)

= 5 - 3

= 2.

⇒a = 2.

Therefore, the first term of the A.P is 2.