In AP $31^{s t}$ terms is 38 and $16^{t h}$ term is 73. Find a.

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Solution

Given,

$a_{n} = a + (n - 1) d$

$a_{31} = a + 30 d = 38$ ........(1)

$a_{16} = a + 15 d = 73$ .........(2)

subtract (1) and (2), we get,

$15 d = - 35$

$d = - \frac{7}{3}$

From (2)

$a = 73 - 15 (- \frac{7}{3})$

$= 73 + \frac{105}{3}$

$= \frac{324}{3}$

$∴ a = 108$

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31^{s t}

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