Question

if the sum of the first
m terms of an AP is sm²+sm, find the common difference​

Answer 1

$Given \:sum \: of \: first \: \pink{m} \:terms :$

$\boxed{\orange {S_{m} = sm^{2} + sm }}\: --(1)$

$i ) If \: m = 1$

$\implies S_{1} = s\times 1^{2} + s \times 1$

$= s + s$

$= 2s$

$ii ) If \: m = 2$

$\implies S_{2} = s\times 2^{2} + s \times 2$

$= 4s + 2s$

$= 6s$

$Now, First \:term (t_{1}) = S_{1} = 2s$

$Second \:term (t_{2}) = S_{2} - S_{1}$

$= 6s - 2s$

$= 4s$

$\therefore \red{ Common \: difference (d) }$

$= t_{2} - t_{1}$

$= 4s - 2s$

$= 2s$

Therefore.,

$\red{ Common \: difference (d) } \green {= 2s}$

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