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

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Solution

The correct option is 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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If the 7th term of a harmonic progression is 8 and the 8th term is 7, then its 15th term is

The correct option is D Obviously, 7th term of corresponding A.P is 18 and 8th term will be 17. a + 6d = 18 and a+7d = 17 Solving these, we get d = 156 and a = 156 Therefore 15th term of this A.P. = 156+14×156 = 1556 Hence the required 15th term of the H.P. is 5615

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