In an A.P. if common difference is 2, sum of n terms is 49,7th term is 13, then n = ………………
In an A.P. if common difference is 2, sum of n terms is 49,7th term is 13, then n = ………………
A) 7
B) 0
C) 13
D) 5
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Correct option is (A) 7
Given that common difference is d = 2
Sum of n terms is \(S_n=49\)
\(7^{th}\) term is \(a_7=13\)
\(\Rightarrow a+6d=13\) \((\because a_7=a+(7-1)d=a+6d)\)
\(\Rightarrow a+12=13\) \((\because d=2)\)
\(\Rightarrow a=13-12=1\)
Now, \(S_n=49\)
\(\Rightarrow\frac n2[2a+(n-1)d]=49\)
\(\Rightarrow\frac n2[2\times1+(n-1)2]=49\)
\(\Rightarrow n[2+2n-2]=49\times2\)
\(\Rightarrow2n^2=49\times2\)
\(\Rightarrow n^2=49\)
\(\Rightarrow n=7\)
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