First slide

Harmonic Progression

Question

$The 5^{th} and 11^{th} terms of an H.P are \frac{1}{45} and \frac{1}{69} respectively, then find 16th term$

Moderate

A

$\frac{1}{85}$
B

$\frac{1}{87}$
C

$\frac{1}{89}$
D

$\frac{1}{91}$

Solution

The 5^th and 11^th terms of the corresponding A.P. are 45
and 69 respectively. Let a be the first term and d be the common difference
of the corresponding A.P then, 5^th term =a+4d=45…. (i) and
11^th term = a+10d=69….. (ii)
Solving equations (i) and (ii), we get a=29, d=4 the 16^th term of the A.P= $a + 15 d = 29 + 15 (4) = 89$
Hence, the 16^th term of the H.P = $\frac{1}{89}$

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