Question

Write the sum using sigma notation: −1 + −7 + −13 +...+ −85∑i=1

Answer 1

The sum is given explicitly as:

-1 + -7 + -13 + ... + -85

Each term of the sum belongs to an arithmetic sequence. The common difference is calculated by subtracting two consecutive terms as follows:

d = -7 - (-1) = -6

The first term is a1 = -1.

The general term n for the sequence is:

an = a1 + (n - 1)d

an = -1 + (n - 1)(-6)

Operating:

an = -1 -6n + 6

an = 5 -6n

The sum is:

`\sum_(i=1)^(i=m)(5-6i)`

We calculate the value of m:

am = 5 -6m = -85

5 -6m = -85

Solving for m:

m = 15

Thus, the summation is:

`\sum_(i=1)^(i=15)(5-6i)`