Question

If the 4th and the 7th terms of an HP are 1/2 and 2/7 respectively. Find the first term

Answer 1

EXPLANATION.

4th terms of an Hp = 1/2.

7th terms of an Hp = 2/7.

Nth terms of an Hp.

→ 1/ a + ( n - 1)d.

4th terms of Hp = 1/ a + 3d = 1/2.

a + 3d = 2 ..........(1)

7th terms of Hp = 1/ a + 6d = 2/7.

2 ( a + 6d ) = 7

2a + 12d = 7 ........(2).

From equation (1) and (2) we get,

multiply equation (1) by 2

multiply equation (2) by 1

2a + 6d = 4

2a + 12d = 7

we get,

- 6d = -3

d = 1/2.

Put the value of d = 1/2 in equation (1)

we get,

a + 3(1/2) = 2

a + 3/2 = 2

a = 2 - 3/2

a = 4 - 3 / 2

a = 1/2.

First term = 1/2.

Common difference = 1/2.

Answer 2

Step-by-step explanation:

Hii Mate REFER to the attachment