Sequence And Series Question 7
Question: If the $ 7^{th} $ term of a harmonic progression is 8 and the $ 8^{th} $ term is 7, then its $ 15^{th} $ term is
[MP PET 1996]
Options:
A) 16
B) 14
C) $ \frac{27}{14} $
D) $ \frac{56}{15} $
Show Answer
Answer:
Correct Answer: D
Solution:
Obviously, $ 7^{th} $ term of corresponding A.P. is $ \frac{1}{8} $ and $ 8^{th} $ 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^{th} $ term of this A.P. $ =\frac{1}{56}+14\times \frac{1}{56}=\frac{15}{56} $ Hence the required $ 15^{th} $ term of the H.P. is $ \frac{56}{15} $ .
BETA
