Question

Which summation formula represents the series below? 5 + 7 + 9 + 11

Answer 1

$\bf \displaystyle \stackrel{2\cdot 0+5}{5}~~,~~\stackrel{2\cdot 1+5}{7}~~,~~\stackrel{2\cdot 2+5}{9}~~,~~\stackrel{2\cdot 3+5}{11}~\hspace{10em}\sum_{i=0}^{3}~2i+5$

Answer 2

Answer:

Summation formula will be $\sum_{n=1}^{4}(2n+3)$

Step-by-step explanation:

The given series is 5 + 7 + 9 + 11

As we can see that terms given in the series are having a common difference d = 7 - 5 = 2

Explicit formula of an arithmetic sequence is

$a_{n}=a+(n-1)d$

Where $a_{n}$ = first term of the sequence

n = number of term

d = common difference of the the terms

Now we put the values of a and d in the explicit formula

$a_{n}=5+(n-1)2=5+2n-2=2n+3$

Therefore in the summation notation formula will be

$\sum_{n=1}^{4}(2n+3)$

Therefore the answer is $\sum_{n=1}^{4}(2n+3)$