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Chapter 12: Q. 276 (page 1218)

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

an=鈭�2n+19

Short Answer

Expert verified

The sum is equal to 45.

Step by step solution

01

Step 1. Given Information 

We are given general term of a sequence,

an=鈭�2n+19

The sum of first thirty term is given by,

Sn=n2(a+an)

02

Step 2. Finding the terms 

Puttingn=1 in the general term, we get

a1=鈭�2(1)+19a1=-2+19a1=17

The fifteenth term is given by,

a15=鈭�2(15)+19a15=-30+19a15=-11

03

Step 3. Finding the sum  

Putting the values in formula, we get

S15=152(17+(-11))S15=152(17-11)S15=152(6)S15=15脳3S15=45

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