Question

if fourth term of Hp is 3/4 and seventh term of HP is 2/3. find the tenth term ​

Answer 1

Given ,

1/(a + 3d) = 3/4. and. 1/(a + 6d) = 2/3

=> (a + 3d) = 4/3. &. (a + 6d) = 3/2

so, (by eq.2 - eq.1 we get)

3d = (3/2 - 4/3)

=> d = (9 - 8)/18

=> d = 1/18

put value in equation 1

a = (4/3 - 3/18)

=> a = (4/3 - 1/6)

=> a = (8-1)/6 = 7/6

now,

= (a + 9d)

= (7/6 + 9/18)

= (7/6 + 1/2)

= (7+3)/6

= 10/6

= 5/3

so, 1/(a + 9d) = 3/5

The tenth term is = 3/5 (ans)