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Chapter 12: Q. 13 (page 838)

In Problems 13鈥�16, find each sum.

鈭�k=150(3k)

Short Answer

Expert verified

The sum is :鈭�k=150(3k)=28825

Step by step solution

01

Step 1. Given information

The summation notation of the sequence is :

鈭�k=150(3k)

02

Step 2. Expand the summation by substituting values of k.

鈭�k=1503k=3.1+3.2+3.3+3.4+...........3.50=3+6+9+.....150

Here we can see that difference between successive terms is:

d=6-3=9-6=3is a constant.

Hence the given sequence is an arithmetic sequence.

03

Step 3. To find sum of 50 terms.

First term isa1=3

common difference is:d=3

Last term of the sequence isa50=150

Hence sum of 50 terms is:S50=502(3+150)=25(153)=28825

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