# Find the 12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity.

A partial sum is basically the sum of part of a sequence. Sometimes partial sums are called "Finite Series".

## Answer: The 12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity is -276.

Let's see the type of series given in the question.

**Explanation: **

Given:

Equation is: x = -2i - 10

Putting i = 1, 2, 3, 4, ...,12 in equation x = -2i - 10, we get

- x(1) = -2 - 10 = -12
- x(2) = -4 - 10 = -14
- x(3) = -6 - 10 = -16
- ....
- x(12) = -24 - 10 = -34

The nth partial sum of an arithmetic sequence is given by

S(n) = n [(x(1) + x(n)] / 2

Thus, applying this to our questions, we get

S(12) = 12 (-12 - 34) / 2 = -46 × 6 = -276