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