Respuesta :

mathstudent55

Answer:

1199

Step-by-step explanation:

There are 22 terms in the sum:

23 + 26 + 29 + ... + 80 + 83 + 86 =

= (23 + 86) + (26 + 83) + ... + (53 + 56)

= 109 + 109 + ... + 109

= 11(109)

= 1199

kudzordzifrancis
ANSWER

1199

EXPLANATION

The given series is

[tex]\sum_{n=9}^{30}(3n-4)[/tex]

To find the first term of this series, we put n=9 into the formula.

[tex]a = 3(9) - 4 = 23[/tex]

To find the last term, we put n=30

[tex]l = 3(30) - 4 = 86[/tex]

There are 22 terms from the 9th term to the 30th term

The sum of the consecutive n-terms of an arithmetic series is given by;

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

We substitute n=22, a=23, and l=86 to get;

[tex]S_ {22}= \frac{22}{2} (23 + 86)[/tex]

[tex]S_ {22}= 11 \times 109[/tex]

[tex]S_ {22}= 1199[/tex]

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