Certainly! To find the values of [tex]\( S_4 \)[/tex] and [tex]\( S_5 \)[/tex] for the given function [tex]\( S_n = 2n + 5 \)[/tex], we need to substitute the values of [tex]\( n \)[/tex] into the function one by one. Here’s the step-by-step solution:
1. Finding [tex]\( S_4 \)[/tex]:
- Start with the given function: [tex]\( S_n = 2n + 5 \)[/tex].
- Substitute [tex]\( n = 4 \)[/tex] into the function:
[tex]\[
S_4 = 2 \cdot 4 + 5
\][/tex]
- Perform the multiplication first:
[tex]\[
2 \cdot 4 = 8
\][/tex]
- Now add 5 to the result:
[tex]\[
8 + 5 = 13
\][/tex]
- Therefore, the value of [tex]\( S_4 \)[/tex] is 13.
2. Finding [tex]\( S_5 \)[/tex]:
- Again, start with the given function: [tex]\( S_n = 2n + 5 \)[/tex].
- Substitute [tex]\( n = 5 \)[/tex] into the function:
[tex]\[
S_5 = 2 \cdot 5 + 5
\][/tex]
- Perform the multiplication first:
[tex]\[
2 \cdot 5 = 10
\][/tex]
- Now add 5 to the result:
[tex]\[
10 + 5 = 15
\][/tex]
- Therefore, the value of [tex]\( S_5 \)[/tex] is 15.
So, the values are:
- [tex]\( S_4 = 13 \)[/tex]
- [tex]\( S_5 = 15 \)[/tex]
