Question

The given series has six terms. What is the sum of the terms of the series? 1 + 3 + 5 + . . . + 11

Answer 1

The rule is +2, so first we find the other two terms.

5 + _ + _ + 11

To find them, add 2 to 5, which gives us 7, so the 4th term is 7, and then add 7 +2, which gives 9, so 9 is the 5th.

Now add all: 1 + 3 + 5 + 7 + 9 + 11 = 36

Your answer is 36.

Answer 2

Answer:  The required sum of the terms is 36.

Step-by-step explanation:  We are given that the following series has six terms :

1  +  3  +  5  +  . . .  +  11.

We are to find the sum of the terms of the series.

We see the following pattern in the consecutive terms of the series :

$3-1=5-3= ~~.~~.~~.~~=2.$

So, the given series is an ARITHMETIC series with fist term 1 and common difference 2.

We know that

the sum of first n terms of an arithmetic series with first term a and common difference d is given by

$S_n=\dfrac{n}{2}(2a+(n-1)d).$

For the given series,

first term, a = 1   and   common difference, d = 2.  

Therefore, the sum of first six terms will be

$S_6=\dfrac{6}{2}(2\times 1+(6-1)\times2)=3(2+5\times2)=3(2+10)=3\times12=36.$

Thus, the required sum of the terms is 36.