Consider the arithmetic series: 1 + 9 + 17 + 25 + ...
Write a formula for the sum of the first n terms in this series.
A) 4n^2 - 3n
B) 6n^2 - 7n
C) 8n^2 - 5n
D) 10n^2 - n
The formula for the sum of n terms in an arithmetic progression is: S = n/2 * (2a + (n-1)d) Here, the common difference, d, is 8 and the first term, a, is 1. Substituting these into the formula, we get:
S = n/2 * (2*1 + 8(n - 1)) S = n + 4n² - 4n S = 4n² - 3n The answer is A.
