If $7^{t h}$ and $13^{t h}$ terms of an AP be 34 and 64, then its $18^{t h}$ term is :

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Solution

The correct option is C 89
We know that,

$x_{m} - x_{n} = (m - n) d$

$∴ x_{13} - x_{7} = (13 - 7) d$

$64 - 34 = 6 d$

$30 = 6 d$

$\Rightarrow d = 5$

$18^{t h}$ term is

$x_{18} = x_{13} + 5 d$

$x_{18} = 64 + 5 (5)$

$x_{18} = 64 + 25 = 89$

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