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

Question

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Respuesta :

kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-05-04T11:03:27+02:00

Answer:

983497

step-by-step explanation:

The sum formula of arithmetic sequence is given by:

[tex]S_n = \frac{n}{2}(2a_1 +(n - 1)d[/tex]

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

From the given information

[tex]d = - 1 -( - 5) = - 1 + 5 = 4[/tex]

[tex]a_1 = - 5 \: and \: n = 703[/tex]

By substitution we obtain:

[tex]S_{703}= \frac{703}{2}(2( - 5) +(703- 1)4)[/tex]

[tex]S_{703}= \frac{703}{2}( - 10 + 2808)[/tex]

[tex]S_{703}= \frac{703}{2}(2798)[/tex]

[tex]S_{703}=98397[/tex]

alinakincsem alinakincsem · Answer 2 · 2019-05-04T11:36:04+02:00

Answer:

S = 983,497

Step-by-step explanation:

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

[tex]-5, -1, 3, 7, ...[/tex]

Finding the common difference [tex]d[/tex] = [tex]-1-(-5)[/tex] = [tex]4[/tex]

[tex]a_1=-5[/tex]

[tex]a_n=?[/tex]

[tex]a_n=a_1+(n-1)d[/tex]

[tex] a_n = - 5 + ( 7 0 3 - 1 ) 4 [/tex]

[tex] a _ n = 2803 [/tex]

Finding the sum using the formula [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex].

[tex]S_n = \frac{703}{2}(-5+2803)[/tex]

S = 983,497