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Chapter 11: Q13. (page 586)

Find the first three terms of each arithmetic series described.

n=8,an=36,Sn=120

Short Answer

Expert verified

The first three terms are-6, 0, 6.

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is n=8,an=36,Sn=120.

02

Step 2. Calculation.

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

Sn=n2(a1+an)

Here, n=8,an=36,Sn=120

Plugging the values:

Sn=n2(a1+an)120=82(a1+36)120=4(a1+36)a1+36=30a1=30鈭�36a1=鈭�6

The nth term of an arithmetic series is given by

an=a1+(n鈭�1)d

Here a1=鈭�6,an=36,n=8a1=鈭�6,an=36,n=8

Plugging the values:

an=a1+(n鈭�1)d36=鈭�6+(8鈭�1)d7d=36+67d=42d=6

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

Hence,

The second term of the series is 鈭�6+6=0

The third term of the series is 0+6=6

03

Step 3. Conclusion.

Hence, the first three terms are -6, 0, 6.

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