Find the sum Sn of the first terms of : 1+3+5+...+(2n-1)

Question

Sum of n terms of an arithmetic sequence formula is Sn=n(a1+a2) divided by @

Answer 1

S[N}= SUM(2N-1) where N=1 to n.

2SUM(N)-n=2n(n+1)/2-n=n^2+n-n=n^2, so sum to n terms is just n^2.

[Sum of natural numbers 1, 2, 3, etc: 1+2+3+...+n=(1+n)+(2+n-1)+(3+n-2)+... Each pair adds up to n+1 and there are n/2 such pairs; hence sum of them = n(n+1)/2 whether n is even or odd.]