Question

If the 2nd term of an H.P. is 3/5 and the 6^th firm is 1/3. Find the value of its 10^th term.
1. 1/7
2. 1/13
3. 3/13
4. 3/11

Answer 1

Correct Answer - Option 3 : 3/13

Given∶

2nd term of a H.P. = 3/5

6th term of a H.P. = 1/3

Formula Used∶

Terms of a H.P. = 1/a, 1/a + d, 1/a + 2d..........1/a +(n - 1)d

Calculation∶

2nd term of a H.P. = 3/5

⇒ 1/a + d = 3/5 

⇒ a + d = 5/3      (1)

6^th term of a H.P. = 1/3 

⇒ 1/a + 5d = 1/3

⇒ a + 5d = 3      (2)

On subtract eq.(2) from (1), we get

⇒ - 4d = - 4/3

⇒ d = 1/3

Put d = 1/3 in eq. (1)

a + 1/3 = 5/3

⇒ a = 4/3

Then, 10th term of an A.P. = a + 9d

⇒ a + 9d = 4/3 + 9 × 1/3 = 13/3

So, 10^th term of a H.P. = 3/13

∴ The required term is 3/13.