Find the sum.
--3 + 1 + 5 + 9 + 13 + ... + (4n - 7)

Question

Quizplus · Accepted Answer

This sequence is an arithmetic sequence with the first term $a_1 = -3$ and a common difference $d = 4$. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $a_n = -3 + (n - 1)4 = 4n - 7$, which matches the last term given in the question. The sum of the first n terms of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$. Substituting the values, we get $S_n = \frac{n}{2}(-3 + 4n - 7) = \frac{n}{2}(4n - 10) = n(2n - 5)$, which corresponds to choice A.

Find the Sum. --3 + 1 + 5 + 9 + 13