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If the sum of first p terms of an A.P is ap2 +bp,find its common difference

Posted by Sushant Thareja 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We are given that sum of first p terms of this AP
S_p= ap² + bp
Let the first term= x and common difference = d
{tex}{\mathrm S}_1=\mathrm a(1)^2+\mathrm b(1)=\mathrm a+\mathrm b{/tex}
So first term x = a+b
Now S₂ = a(2)² + b(2)
S₂ = 4a + 2b
,{tex}\mathrm{So}\;{\mathrm s}_2={\mathrm a}_1+{\mathrm a}_2=\mathrm x+\mathrm x+\mathrm d=4\mathrm a+2\mathrm b{/tex}
2x + d = 4a+2b
2(a+b)+d = 4a+2b
2a+2b+d=4a+2b
d=4a+2b-2a-2b
d = 2a
Therefore, the common difference of the given AP is 2a.

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