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Chapter 11: Q9. (page 586)

Find the sum of each arithmetic series.

38+35+32+...+2

Short Answer

Expert verified

The sum of the arithmetic series is260.

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is 38+35+32+...+2.

02

Step 2. Calculation.

The difference between the terms is 35鈭�38=鈭�3

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

Here, localid="1648547769020" a1=38,d=鈭�3,an=2

Plugging the values:

an=a1+(n鈭�1)d2=38+(n鈭�1)(鈭�3)(n鈭�1)(鈭�3)=2鈭�38(n鈭�1)(鈭�3)=鈭�36n鈭�1=12n=12+1n=13

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

Sn=n2(a1+an)

Here, localid="1648547799867" a1=38,n=13,an=2

Plugging the values:

Sn=n2(a1+an)S13=132(38+2)S13=132(40)S13=13(20)S13=260

03

Step 3. Conclusion.

Hence, the sum is 260.

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Most popular questions from this chapter

Find the indicated term of each arithmetic sequence.

a1=20,d=4,n=81

Find the first three terms of each arithmetic series described.

n=8,an=36,Sn=120

Find Snfor each arithmetic series described.

d=5,n=16,an=72

Write an equation for the nth term of each arithmetic sequence.

7, 16, 25, 34, ....

Find the arithmetic means in each sequence.

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