Question

For an AP of 14 terms, find the value of $a_9$, if $a_4+a_{11}=118$ and $a_6=56$.

• A. 62
• B. 58
• C. 64
• D. 70

Answer 1

The correct option is A 62

For an AP, $a_1,a_2,a_3,.......,a_n$

$a_1+a_n=a_2+a_{n-1}=a_3+a_{n-2}$ and so on.

By observing we get to know that sum of terms are equal , if its sum of position value are equal.

Here in this AP , $a_1+a_{14}=a_2+a_{13}=a_3+a_{12}$ and so on.

$\therefore a_4+a_{11}=a_6+a_9$

Given $a_4+a_{11}=118$ and $a_6=56$.

$\Rightarrow 118=56+a_9$

$\Rightarrow a_9=118-56=62$