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Chapter 12: Q. 275 (page 1218)

In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.

an=4n+7

Short Answer

Expert verified

The sum is equal to 585.

Step by step solution

01

Step 1. Given Information 

We are given general term of a sequence,

an=4n+7

The sum of first thirty term is given by,

Sn=n2(a+an)

02

Step 2. Finding the terms 

Putting n=1in the general term, we get

a1=4(1)+7a1=4+7a1=11

The fifteenth term is given by,

a15=4(15)+7a15=60+7a15=67

03

Step 3. Finding the sum  

Putting the values in formula, we get

S15=152(11+67)S15=152(78)S15=15脳39S15=585

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