If a_1,a_2,a_3,,a_n, are in A.P.

Question

If $a_1,a_2,a_3,\ldots,a_n,\ldots$ are in A.P. such that $a_4-a_7+a_{10}=m$, then the sum of the first 13 terms of this A.P. is:

Accepted Answer

Let $d$ be the common difference: $m=a_4-a_7+a_{10}=(a_7-3d)-a_7+(a_7+3d)=a_7$.

$$S_{13}=\frac{13}{2}(a_1+a_{13})=\frac{13}{2}(2a_7)=13a_7=13m.$$

Solutions · 1