Question

If n is odd, then (1+3 +5 + 7 + ... to n terms) is equal to: 

A. (n² +1) 

B. (n² —1) 

C. n² 

D. (2n² +1)

Answer 1

We know that,In the given series,a = 1, d = 3 - 1 = 2

Sum of n numbers = \(\frac{n}{2}[2(1)+(n-1)d]\)

= \(\frac{n}{2}[2\,+(n-1)2]\)

= \(\frac{n}{2}[2+2n-2]\)

= \(\frac{n}{2}\times2n\)

= n²

Hence,

Option (C) is the correct option.