The sum of first n odd natural numbers in
A. 2n - 1
B. 2n + 1
C. n2
D. n2 - 1
Answer: Option C
Solution(By Examveda Team)
1, 3, 5, 7, ........ are n odd numbersWhere a = 1, and d = 2
$$\eqalign{ & \therefore {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2}\left[ {2 \times 1 + \left( {n - 1} \right) \times 2} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2}\left[ {2 + 2n - 2} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{n}{2} \times 2n \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {n^2} \cr} $$
Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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