Question

Find the sum of the first 33 terms of the arithmetic sequence whose first term is 3 and whose 33rd term is -253. please help. and i want to know how to get the answer

Answer 1

All right, if we have an arithmetic sequence, it must be of the form:
\[
a_n=kn+b
\]For some \(k, b\).
But, since it is a straight line, we can use the average formula and multiply this by the number of items to obtain the total of the sequence. So, we have:
\[
\frac{-253+3}{2}(33)=-4125
\]Which should be our sum.

In general, for any arithmetic sum, we have:
\[
\frac{n(a_1+a_n)}{2}=S_n
\]