Question

If 1/a,1/b,1/c are in A.P then b=?
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Answer 1

Given,

if 1/a , 1/b , 1/c are in a.p

We know that,

If a,b,c are in a.p then,

second term - first term = third term - second term

$b - a = c - b \\ b + b = c + a \\ 2b = a + c$

2 ( second term ) = first term + third term

first term = 1/a

second term = 1/b

third term = 1/c

$2( \frac{1}{b} ) = \frac{1}{a} + \frac{1}{c } \\ \frac{2}{b} = \frac{a + c}{ac} \\ 2(ac) = b(a + c) \\ 2ac = b(a + c) \\ b(a + c) = 2ac \\ b = \frac{2ac}{a + c}$