If a - 14, a - 2, a + 34 are in G.P, find the value of a.

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Solution

${(a - 2)}^{2}$ = (a - 14) (a + 34)

$a^{2}$ - 4a + 4 = $a^{2}$ + 20a - 14 $\times$ 34

24a = 14 $\times$ 34 + 4

a = $\frac{14 \times 34 + 4}{24}$

= 20

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