If the sum of n terms of an A.P is 4n^2 + 5n, then common difference is
If the sum of n terms of an A.P is 4n2 + 5n, then common difference is
A) 8
B) 0
C) 4
D) 6
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Correct option is (A) 8
Given that sum of n terms of an A.P. is \(4n^2+5n.\)
\(\therefore\) \(S_n=4n^2+5n\)
\(\therefore a_1=S_1=4.1^2+5.1\)
\(=4+5=9\)
\(\&\;S_2=4.2^2+5.2\)
\(=16+10=26\)
\(\Rightarrow a_1+a_2=26\) \((\because S_2=a_1+a_2)\)
\(\Rightarrow a_2=26-a_1\)
\(=26-9=17\)
Now, \(d=a_2-a_1\)
\(=17-9=8\)
Hence, common difference of given A.P. is 8.
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