Answer:
[tex]S_4=50[/tex]
Step-by-step explanation:
Sum Of Arithmetic Sequence
Given an arithmetic sequence
[tex]a_1,\ a_1+r,\ a_1+2r,....,\ a_1+(n-1)r[/tex]
The sum of the n first terms is
[tex]\displaystyle S_n=\frac{(a_1+a_n)n}{2}[/tex]
Or equivalently
[tex]\displaystyle S_n=\frac{[2a_1+(n-1)r]n}{2}[/tex]
The given sequence is
5, 8, 11 ...
We can see the common difference between terms is r=3
We are asked to find the sum of the terms 2 to 5, it means that
[tex]a_1=8, n=4, r=3[/tex]
[tex]\displaystyle S_4=\frac{[2(8)+(4-1)3]4}{2}[/tex]
[tex]\displaystyle S_4=\frac{100}{2}[/tex]
[tex]\boxed{S_4=50}[/tex]
