Sequence And Series Question 537
Question: If the $ n^{th} $ term of an A.P. be $ (2n-1) $ , then the sum of its first $ n $ terms will be
Options:
A) $ n^{2}-1 $
B) $ {{(2n-1)}^{2}} $
C) $ n^{2} $
D) $ n^{2}+1 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ T_{n}=2n-1 $ First term $ a=2.1-1=1 $ Second term $ b=2\ .\ 2-1=3 $ Third term $ c=2\ .\ 3-1=5 $ Therefore sequence is $ 1,\ 3,\ 5,…….2n-1 $ . Now sum of the first $ n $ terms is $ S_{n}=\frac{n}{2}[a+l] $ $ =\frac{n}{2}[1+2n-1]=\frac{n}{2}\ .\ 2n=n^{2} $ Aliter: Since $ T_{n}=2n-1 $
$ \Rightarrow S_{n}=\Sigma T_{n}=2\Sigma n-\Sigma \ 1=n(n+1)-n=n^{2} $
BETA
