Sum of terms

Algebra Level pending

An arithmetic progression has $13$ terms. The sum of the odd terms $(a_1+a_3+a_5…)$ is $98$ . The sum of the even terms $(a_2+a_4+a_6…)$ is $84$ . Find the sum of the third term to the eleventh term.

The answer is 126.

1 solution

A Former Brilliant Member
Sep 22, 2017

$s_{(odd)}=\dfrac{7}{2}(a_1+a_{13})$ $\implies$ $98(2)=7(a_1+a_{13})$ $\implies$ $a_1+a_{13}=28$

$s_{(even)}=\dfrac{6}{2}(a_2+a_{12})$ $\implies$ $84=3(a_2+a_{12})$ $\implies$ $a_2+a_{12}=28$

$s=s_{(odd)}+s_{(even)}=98+84=182$

The sum of the third term to the eleventh term is $182-28-28=$ $\color{#D61F06}\boxed{126}$ .

Sum of terms

The answer is 126.

1 solution

0 pending reports