If a1, a2, a3, ......., an, ..... are in A.P. such that a4- a7 + a10 = m, then the sum of first 13 terms of this A.P., is :

Question

If a1, a2, a3, ......., an, ..... are in A.P. such that a4- a7 + a10 = m, then the sum of first 13 terms of this A.P., is : (A) 10 m (B) 12 m (C) 13 m (D) 15 m

Tardigrade Admin · Accepted Answer

If d be the common difference, then m=a4-a7+a10=a4-a7+a7+3d=a7 S13=(13/2)[a1+a13]=(13/2)[a1+a7+6d] =(13/2)[2a7]=13a7=13 m

Q. If $a_{1}, a_{2}, a_{3}, ......., a_{n}, .....$ are in $A . P$ . such that $a_{4} - a_{7} + a_{10} = m,$ then the sum of first $13$ terms of this $A . P$ ., is :

10 m

12 m

13 m

15 m

If $d$ be the common difference, then
$m = a_{4} - a_{7} + a_{10} = a_{4} - a_{7} + a_{7} + 3 d = a_{7}$
$S_{13} = \frac{13}{2} [a_{1} + a_{13}] = \frac{13}{2} [a_{1} + a_{7} + 6 d]$
$= \frac{13}{2} [2 a_{7}] = 13 a_{7} = 13 m$

Q. If a1​,a2​,a3​,.......,an​,..... are in A.P. such that a4​−a7​+a10​=m, then the sum of first 13 terms of this A.P., is :