Respuesta :
[tex] \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 [/tex]
Answer:
Summation formula will be [tex]\sum_{n=1}^{4}(2n+3)[/tex]
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
[tex]a_{n}=a+(n-1)d[/tex]
Where [tex]a_{n}[/tex] = 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
[tex]a_{n}=5+(n-1)2=5+2n-2=2n+3[/tex]
Therefore in the summation notation formula will be
[tex]\sum_{n=1}^{4}(2n+3)[/tex]
Therefore the answer is [tex]\sum_{n=1}^{4}(2n+3)[/tex]
