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Chapter 11: Q10. (page 586)

Find the sum of each arithmetic series.

鈭�n=17(2n+1)

Short Answer

Expert verified

The sum of the arithmetic series is63.

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is 鈭�n=17(2n+1).

02

Step 2. Calculation.

From the summation, the number of terms is n=7

The first term is given by plugging n=1:

an=2n+1a1=2(1)+1a1=2+1a1=3

The last term is given by plugging n=7:

an=2n+1a7=2(7)+1a7=14+1a7=15

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

Sn=n2(a1+an)

Here, a1=3,n=7,an=15

Plugging the values:

Sn=n2(a1+an)S7=72(3+15)S7=72(18)S7=7(9)S7=63

03

Step 3. Conclusion.

Hence, the sum is 63.

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Find the first five terms of each arithmetic sequence described.

a1=2,d=13

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