Question

if the sum of first m terms of an AP is amsquare+bm find its common difference

Answer 1

Solution:

Given: $S_{m} = am^2+bm$

∴[tex]S _{1} =a(1)^2+b(1) [/tex]=$a+b=a _{1}=\ \textgreater \ a _{1} =a+b .....(i)$

$S _{2} =a(2)^2+b(2)=4a+2b=a _{1}+a_{2}$
$a+b+a_2=4a+2b=\ \textgreater \ a_2=3a+b$
$a_2=a+d$
[tex]3a+b=a+b+d [/tex]
∴$d=2a$