Question

Write the series -25-22-19 +....for 14 terms using summation notation.

Answer 1

`\sum_(n=1)^(14)(3n-28)`

Explanation:

The given series is

`-25-22-19+...`

The the first term of the sequence is;

`a_1=-25`

The constant difference is;

`d=-22--25`

`d=3`

The nth term of the series is

`a_n=a_1+d(n-1)`

`a_n=-25+3(n-1)`

`a_n=-25+3n-3`

`a_n=3n-28`

Using the summation notation, we can write the series as;

`\sum_(n=1)^(14)(3n-28)`