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Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.

Respuesta :

irspow
The sum of an arithmetic sequence is the average of the first and last terms time the number of terms...

So the first term is 3+3 and the last term is 3(13)+3

So the sum is:

13(6+42)/2

312

Answer:

The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.

Step-by-step explanation:

The given expression is

[tex]3n+3[/tex]

For n=1,

[tex]3(1)+3=6[/tex]

For n=2,

[tex]3(2)+3=9[/tex]

For n=3,

[tex]3(3)+3=12[/tex]

The required AP is

[tex]6, 9, 12, ...[/tex]

Here first term is 6 and common difference is 3.

The sum of n terms of an AP is

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

[tex]S_{13}=\frac{13}{2}[2(6)+(13-1)(3)][/tex]

[tex]S_{13}=\frac{13}{2}[12+36][/tex]

[tex]S_{13}=312[/tex]

Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.