Question

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

Answer 1

Let $d$ be the common difference of the given A.P.

Given in the A.P., $a_4-a_7+a_{10}=m$

or, $a_1+3d-(a_1+6d)+a_1+9d=m$

or, $a_1+6d=m$......(1).

Now the sum of first $13$ terms of the A.P. is

$\frac{13}{2}(2a_1+12d)$

$=13(a_1+6d)$

$=13m$.[ [Using (1)]