Consider the arithmetic series:

2 + 6 + 10 + ... + (4n - 2) + ...

Write a formula for the sum of the first n terms in this series

Question

Consider the arithmetic series: 

2 + 6 + 10 + ... + (4n - 2) + ...

Write a formula for the sum of the first n terms in this series

anonymous · Answer

summation of (4n-2)

directrix · Answer

Gotta learn those formulas or how to generate them. I'll provide a link at the bottom. The sum of the first n terms of the arithmetic series is the number of terms N times the sum of the first and nth terms, all divided by 2. Sum = n [ (2) + 4(n - 2)] / 2 = n [ 2 + 4n - 8] / 2 = n [ 4n - 6] /2 = n ( 2n - 3) or 2n^2 -3n. (Check the arithmetic.) http://regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm