If $9^{t h}$ term of an A.P. is $47$ and $16^{t h}$ term is $82$ , then the general term is

9 n + 2

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6 n - 7

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5 n + 2

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none

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Solution

The correct option is D $5 n + 2$
$a_{9} = a + 8 d = 47$ ........(1)
$a_{16} = a + 15 d = 82$ .....(2)
Subtract eq (1) by (2)
$7 d = 35$
$∴ d = 5$
$a + 8 d = 47$
$a + 8 \times 5 = 47$
$∴ a = 7$
Hence general term is $a_{n} = a + (n - 1) d = 5 n + 2$

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