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Chapter 11: Q8. (page 586)

Find the sum of each arithmetic series.

5+11+17+...+95

Short Answer

Expert verified

The sum of the arithmetic series is800.

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is5+11+17+...+95 .

02

Step 2. Calculation.

The difference between the terms is11鈭�5=6

The nth term of an arithmetic series is given by an=a1+(n鈭�1)d

Here, a1=5,d=6,an=95

Plugging the values:

an=a1+(n鈭�1)d95=5+(n鈭�1)(6)(n鈭�1)(6)=95鈭�5(n鈭�1)(6)=90n鈭�1=15n=15+1n=16

The sum Sn of the first n terms of an arithmetic series is given by

Sn=n2(a1+an)

Here, a1=5,n=16,an=95

Plugging the values:

Sn=n2(a1+an)S16=162(5+95)S16=8(100)S16=800

03

Step 3. Conclusion.

Hence, the sum is 800.

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Most popular questions from this chapter

68 is the ___?__ th term of the arithmetic sequence -2, 3, 8, ... .

Find the indicated term of each arithmetic sequence.

a43 for 5, 9, 13, 17, 鈥�

WRITING IN MATH

Answer the question that was posed at the beginning of the lesson.

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