If the 7th term of a harmonic progression is 8 and the 8th term is 7, then its 1

Question

If the

7^{t h}

term of a harmonic progression is 8 and the

8^{t h}

term is 7, then its

15^{t h}

term is

Options:

A . 16

B . 14

C . 2714

D . 5615

Answer: Option D
:
D
Obviously,

7^{t h}

term of corresponding A.P is

\frac{1}{8}

and

8^{t h}

term will be

\frac{1}{7}

. a + 6d =

\frac{1}{8}

and a+7d =

\frac{1}{7}

Solving these, we get d =

\frac{1}{56}

and a =

\frac{1}{56}

Therefore

15^{t h}

term of this A.P.
=

\frac{1}{56} + 14 \times \frac{1}{56}

\frac{15}{56}

Hence the required

15^{t h}

term of the H.P. is

\frac{56}{15}

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