Question

In a H.P. the 7^th term is 9 and its ninth term is 7, Find its 63rd term and hence the p^th term
1. 1/52 ; 1/(3n-1)]
2. 63 ; 1/n
3. 1/49 ; 1/[3n-11]
4. 1 ; 63/n

Answer 1

Correct Answer - Option 4 : 1 ; 63/n

Given∶

In a H.P., 7^th term = 9

9^th term = 7

Formula Used∶

General form of H.P. is 1/a, 1/a + d, 1/ a + 2d, .........

n^th term of H.P. = 1/[a + (n - 1)d]

Calculation∶

7^th term of a H.P.,

⇒  1/a + 6d = 9

⇒  a + 6d = 1/9      (1)

9^th term of a H.P.,

⇒  1/a + 8d = 7

⇒  a + 8d = 1/7      (2),

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

2d = (1/7 - 1/9) = 2/63

⇒ d = 1/2 × 2/63 = 1/63

Putting d = 1/63 in eq.(1), we get

a + [6 × 1/63] = 1/9

⇒ a + 2/21 = 1/9

⇒ a = (1/9 - 2/21)

⇒ a = (7 - 6)/63 = 1/63

Thus, a = 1/63 = 1/63

So, 63^rd term of a H.P.,

1/[a + (n - 1)d] = 1/[1/63 + (n - 1)1/63]

1/[a + (n - 1)d] = 1/n/63 = 63/n

∴ 63^rd term of a H.P. is 1 and nth term is 63/n.