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In an HP, the fourth term is two times the eighth term. The first term of the HP will be?

In an HP, the fourth term is two times the eighth term. The first term of the HP will be? Correct Answer 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 nth term in HP = 1/(a + (n - 1)d)

⇒ 1/na

The nth term in HP = First term/n

First term = n × nth term

Option 4 is correct

Important Points

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

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