Find the indicated sum.
-7 + 3 - 1 + . . . - 153

Question

Quizplus · Accepted Answer

This sequence is an arithmetic sequence with the first term $a_1 = 7$, common difference $d = 3 - 7 = -4$, and the last term $a_n = -153$. To find the sum, we first need to determine the number of terms $n$. We can use the formula for the $n$th term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$. Substituting the given values, we get $-153 = 7 + (n - 1)(-4)$. Solving for $n$ gives us $n = 41$. Then, we use the sum formula for an arithmetic sequence: $S_n = \frac{n}{2}(a_1 + a_n)$. Substituting the known values, we get $S_n = \frac{41}{2}(7 - 153)$, which simplifies to $S_n = -2993$.

Find the Indicated Sum