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Chapter 11: Q7. (page 586)

Find Snfor each arithmetic series described.

d=5,n=16,an=72

Short Answer

Expert verified

Snfor the arithmetic series isS16=552 .

Step by step solution

01

Step 1. Given Information.

Given arithmetic series is d=5,n=16,an=72.

02

Step 2. Calculation.

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

Here, d=5,n=16,an=72

Plugging the values:

an=a1+(n鈭�1)d72=a1+(16鈭�1)(5)72=a1+(15)(5)72=a1+75a1=72鈭�75a1=鈭�3

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

Sn=n2(2a1+(n鈭�1)d)

Here, a1=鈭�3,n=16,d=5

Plugging the values:

Sn=n2(2a1+(n鈭�1)d)S16=162(2(鈭�3)+(16鈭�1)(5))S16=8(鈭�6+(15)(5))S16=8(鈭�6+75)S16=8(69)S16=552

03

Step 3. Conclusion.

Hence, the sum is S16=552S16=552.

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