If $7^{t h}$ and $13^{t h}$ terms of an AP be 34 and 64, then its $18^{t h}$ and $25^{t h}$ term is :

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Solution

The correct options are
C 89
D 90
$a_{n} = a + (n - 1) d a + 6 d = 34 - - - (1) a + 12 d = 64 - - - (2) S o l v i n g (1) a n d (2), a = 4 a n d d = 5 a_{18} = 4 + (17) 5 = 89$
Similarly $25^{t h}$ term is,
a_{25} = 4+(24)5=124\)

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