If $7 t h$ and $13 t h$ terms of an $A . P$ . Be $34$ and $64$ , respectively, then its $18 t h$ terms is:

87

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88

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89

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90

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Solution

The correct option is D $89$
The general term of an $A P$ is given by $a_{n} = a + (n - 1) d$ , where $a$ & $d$ are the first and common difference of an $A P$ respectively.
$a_{7} = 34$
$a_{13} = 64$
$a + 6 d = 34$
$a + 12 d = 64$
$- 6 d = - 30$
$d = \frac{30}{6} = 5$
$∴ a = 4.$
$a_{18} = a + 17 d = 4 + 17 (5) = 89$

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If the $7^{t h}$ and $13^{t h}$ terms of an AP are 34 and 64 respectively, then its $18^{t h}$ term would be ____

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