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  4. The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is

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Q. The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is

Sequences and Series

Solution:

$a ; a+9 ; a+18 ; \ldots \ldots$.
Now, $a_1, a_3$ and $a_8$ in G.P. i.e. $a, a+18$ and $a+63$ in G.P.
$\therefore(a+18)^2=a(a+63)=a^2+63 a \Rightarrow a=12 ; d=9$
So, $a_7=a+6 d=12+54=66$.