If d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is …

1.	If d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is ………………A) (225)/2B) 0 C) 15 D) 225
Answer» Correct option is (D) 225 We have d = 2 & \(a_8=15\) \(\therefore a+7d=15\) \((\because a_8=a+(8-1)d=a+7d)\) \(\Rightarrow a+7\times2=15\) \(\Rightarrow a=15-14=1\) \(\therefore\) Sum of 15 terms is \(S_{15}=\frac{15}2[2a+(15-1)d]\) \(=\frac{15}2[2\times1+14\times2]\) \((\because a=1\;\&\;d=2)\) \(=\frac{15}2(2+28)\) \(=\frac{15}2\times30\) \(=15\times15=225\) Correct option is D) 225

If d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is ………………A) (225)/2B) 0 C) 15 D) 225

Answer»

Correct option is (D) 225

We have d = 2 & \(a_8=15\)

\(\therefore a+7d=15\) \((\because a_8=a+(8-1)d=a+7d)\)

\(\Rightarrow a+7\times2=15\)

\(\Rightarrow a=15-14=1\)

\(\therefore\) Sum of 15 terms is \(S_{15}=\frac{15}2[2a+(15-1)d]\)

\(=\frac{15}2[2\times1+14\times2]\) \((\because a=1\;\&\;d=2)\)

\(=\frac{15}2(2+28)\)

\(=\frac{15}2\times30\)

\(=15\times15=225\)

Correct option is D) 225