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Q39.

Expert-verifiedFound in: Page 851

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Partial Sums Find the first six partial sums ${S}_{1},\u200a\u200a{S}_{2},\u200a\u200a{S}_{3},\u200a\u200a{S}_{4},\u200a\u200a{S}_{5},\u200a\u200a{S}_{6}$** **of the sequence whose nth term is given.**

$1,\u200a\u200a3,\u200a\u200a5,\u200a\u200a7,\u200a$**….**

The partial sums are:

$\begin{array}{l}\text{Firstpartialsum}={S}_{1}=1.\\ \text{Secondpartialsum}={S}_{2}=4.\\ \text{Thirdpartialsum}={S}_{3}=9.\\ \text{Fourthpartialsum}={S}_{4}=16.\\ \text{Fifthpartialsum}={S}_{5}=25.\\ \text{Sixth partialsum}={S}_{6}=36.\end{array}$

The given sequence is 1, 3, 5, 7…

We have to find the first six partial sums.

The given sequence is 1, 3, 5, 7…

We see that the terms are increasing by 2.

So, the first 6 terms of these sequence are 1, 3, 5, 7, 9, 11.

Hence,

$\begin{array}{l}\text{Firstpartialsum}={S}_{1}=1.\\ \text{Secondpartialsum}={S}_{2}=1+3=4.\\ \text{Thirdpartialsum}={S}_{3}=1+3+5=9.\\ \text{Fourthpartialsum}={S}_{4}=1+3+5+7=16.\\ \text{Fifthpartialsum}={S}_{5}=1+3+5+7+9=25.\\ \text{Sixth partialsum}={S}_{6}=1+3+5+7+9+11=36.\end{array}$

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