Question

In an HP, the fourth term is two times the eighth term. The first term of the HP will be?
1. Two times the third term.
2. Four times the third term.
3. Eight times the seventh term.
4. Seven times the seventh term.
5.

Answer 1

Correct Answer - Option 4 : Seven times the seventh term.

Calculation:

Let 1/p and 1/q are fourth and eighth term of HP

⇒ 1/p = 2/q

p and q are in AP

p = a + 3d

q = a + 7d

∴ 1/(a + 3d) = 2/(a + 7d)

⇒ a + 7d = 2a + 6d

⇒ d = a

The n^th term in HP = 1/(a + (n - 1)d)

⇒ 1/na

The n^th term in HP = First term/n

First term = n × n^th term

Option 4 is correct

The reciprocals of the terms in an HP will form an AP.