If the sum of n terms of an A.P is 4n2 + 5n, then common difference is

1.	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
Answer» 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. Correct option is A) 8

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

Answer»

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.

Correct option is A) 8