Find x if 1/x+2, 1/x+3 and 1/x+5 are in AP.

Find $x$ if $\frac{1}{x + 2}, \frac{1}{x + 3}$ and $\frac{1}{x + 5}$ are in AP.

Class 10Properties and Selection of AP TermsAlgebra — Sequences

\frac{2}{x + 3} = \frac{1}{x + 2} + \frac{1}{x + 5} = \frac{2 x + 7}{( x + 2 ) ( x + 5 )}

. Cross-multiplying:

2 x^{2} + 14 x + 20 = 2 x^{2} + 13 x + 21

, so

x = 1

. Check:

\frac{1}{3}, \frac{1}{4}, \frac{1}{6}

differ by

- \frac{1}{12}

Answer: C) 1

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