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  4. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

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Q. If $9$ times the $9^{th}$ term of an $A.P$. is equal to $13$ times the $13^{th}$ term, then the $22^{nd} $ term of the $A.P$. is

Sequences and Series

Solution:

Let $1^{st}$ term of $A.P. = a$ and common difference $= d $
Given, $9 \times a_9 = 13 \times a_{13}$
$\Rightarrow 9(a + 8d) = 13(a + 12d)$
$ \Rightarrow 4a + 84d = 0$
$\Rightarrow a + 21 d = 0 $
Now, $a_{22} = a + 21d = 0$