Question

What is the sum of the first 703 terms of the sequence -5, -1, 3, 7, ...?

Answer 1

S = 983,497

Explanation:

We are given the following sequence and we are to find the sum of the first 703 terms of this sequence:

`-5, -1, 3, 7, ...`

Finding the common difference
`d` =
`-1-(-5)` =
`4`

`a_1=-5`

`a_n=?`

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

`a_n = - 5 + ( 7 0 3 - 1 ) 4`

`a _ n = 2803`

Finding the sum using the formula
`S_n = (n)/(2)(a_1+a_n)`.

`S_n = (703)/(2)(-5+2803)`

S = 983,497

Answer 2

983497

Explanation:

The sum formula of arithmetic sequence is given by:

`S_n = (n)/(2)(2a_1 +(n - 1)d`

a_1 is the first term, n is the nth term and d is the common difference

From the given information

`d = - 1 -( - 5) = - 1 + 5 = 4`

`a_1 = - 5 \: and \: n = 703`

By substitution we obtain:

`S_(703)= (703)/(2)(2( - 5) +(703- 1)4)`

`S_(703)= (703)/(2)( - 10 + 2808)`

`S_(703)= (703)/(2)(2798)`

`S_(703)=98397`