How many terms of the series -3 -1 + 1 +..... add up to 165?
The series can be rewritten as follows:
-3 + (-1 + 1) + (-3 + 1) + (-1 + 1) + ...
Simplifying, we get:
-3 + 0 + -2 + 0 + -3 + 0 + -2 + 0 + ...
The terms in the series alternate between -3 and 0. Therefore, we can group the terms as follows:
(-3 + 0) + (-2 + 0) + (-3 + 0) + (-2 + 0) + ...
Each pair of terms adds up to -3, and there are n/2 pairs of terms in the series, where n is the number of terms. Therefore, we can write the following equation:
-3(n/2) = 165
Simplifying, we get:
n = -2(165)/3
n = -110
Since the number of terms must be a positive integer, the answer is none of the given options. This means that there is no solution to the problem, as the series cannot add up to 165.
The terms in the series alternate between -3 and 0. Therefore, we can group the terms as follows:
(-3 + 0) + (-2 + 0) + (-3 + 0) + (-2 + 0) + ...
Each pair of terms adds up to -3, and there are n/2 pairs of terms in the series, where n is the number of terms. Therefore, we can write the following equation:
-3(n/2) = 165
Simplifying, we get:
n = -2(165)/3
n = -110
Since the number of terms must be a positive integer, the answer is none of the given options. This means that there is no solution to the problem, as the series cannot add up to 165.