Question

Partial Sums Find the first six partial sums $S_1, S_2, S_3, S_4, S_5, S_6$ of the sequence whose nth term is given.

$1, 3, 5, 7,$….

Short answer

The partial sums are:

$\begin{array}{l}\text{Firstpartialsum}=S_1=1.\\ \text{Secondpartialsum}=S_2=4.\\ \text{Thirdpartialsum}=S_3=9.\\ \text{Fourthpartialsum}=S_4=16.\\ \text{Fifthpartialsum}=S_5=25.\\ \text{Sixthpartialsum}=S_6=36.\end{array}$

Step-by-step solution

Step 1.  Given

The given sequence is 1, 3, 5, 7…

Step 2.  To determine

We have to find the first six partial sums.

Step 3.  Calculation

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,

$\begin{array}{l}\text{Firstpartialsum}=S_1=1.\\ \text{Secondpartialsum}=S_2=1+3=4.\\ \text{Thirdpartialsum}=S_3=1+3+5=9.\\ \text{Fourthpartialsum}=S_4=1+3+5+7=16.\\ \text{Fifthpartialsum}=S_5=1+3+5+7+9=25.\\ \text{Sixthpartialsum}=S_6=1+3+5+7+9+11=36.\end{array}$