Question

Sum of first n terms of ap is an^2+bn.find its common difference

Answer 1

hope it is helpful for you

Answer 2

Solution:

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Given:

Sum of n terms of an AP is an² + bn ,.

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To find:

The common difference between the terms of the given AP,.

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As, we know that,

$S_n = a + a_2 + a_3,...a_n$

=> $S_n = a + (a+d) + (a+2d),...(a+(n-1)d)$

If n = 1,

=>$S_1 = a_1 = a$

=> a(1)² + b(1)

=> a + b,..

∴ $a_1 =a+b$,..

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If n = 2,

=> $S_2 = a_1 + a_2$

=> $S_2 = a + (a + d)$

=> a(2)² + b(2) = a+b + a + b  + d

=> 4a + 2b = 2a + 2b + d

=> 2a + 2b + d = 4a + 2b

=> d = 2a,.

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∴ Common difference of the AP is 2a,.

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