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Chapter 11: Q12. (page 586)

Find the first three terms of each arithmetic series described.

a1=11,an=110,Sn=726

Short Answer

Expert verified

The first three terms are11, 20, 29.

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is a1=11,an=110,Sn=726.

02

Step 2. Calculation.

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

Sn=n2(a1+an)

Here, a1=11,an=110,Sn=726

Plugging the values:

Sn=n2(a1+an)726=n2(11+110)726=n2(121)n2=6n=12

The nth term of an arithmetic series is given by

an=a1+(n鈭�1)d

Here a1=11,an=110,n=12

Plugging the values:

an=a1+(n鈭�1)d110=11+(12鈭�1)d11d=110鈭�1111d=99d=9

Adding the common difference d to a term gives the next term.

Hence,

The second term of the series is 11+9=20

The third term of the series is 20+9=29

03

Step 3. Conclusion.

Hence, the first three terms are 11, 20, 29.

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