Sure! Let's break down the problem step by step to generate the first 5 numbers in the sequence defined by the function [tex]\( f(n) = 99 - 5(n-1) \)[/tex].
### Step-by-Step Solution:
1. Understanding the Sequence Formula:
- The function we are given is [tex]\( f(n) = 99 - 5(n-1) \)[/tex].
- This is an arithmetic sequence where [tex]\( a = 99 \)[/tex] (the first term) and [tex]\( d = -5 \)[/tex] (the common difference).
2. Calculate the First Term ([tex]\( n = 1 \)[/tex]):
[tex]\[
f(1) = 99 - 5(1-1) = 99 - 5 \cdot 0 = 99
\][/tex]
So, the first term in the sequence is [tex]\( 99 \)[/tex].
3. Calculate the Second Term ([tex]\( n = 2 \)[/tex]):
[tex]\[
f(2) = 99 - 5(2-1) = 99 - 5 \cdot 1 = 99 - 5 = 94
\][/tex]
So, the second term in the sequence is [tex]\( 94 \)[/tex].
4. Calculate the Third Term ([tex]\( n = 3 \)[/tex]):
[tex]\[
f(3) = 99 - 5(3-1) = 99 - 5 \cdot 2 = 99 - 10 = 89
\][/tex]
So, the third term in the sequence is [tex]\( 89 \)[/tex].
5. Calculate the Fourth Term ([tex]\( n = 4 \)[/tex]):
[tex]\[
f(4) = 99 - 5(4-1) = 99 - 5 \cdot 3 = 99 - 15 = 84
\][/tex]
So, the fourth term in the sequence is [tex]\( 84 \)[/tex].
6. Calculate the Fifth Term ([tex]\( n = 5 \)[/tex]):
[tex]\[
f(5) = 99 - 5(5-1) = 99 - 5 \cdot 4 = 99 - 20 = 79
\][/tex]
So, the fifth term in the sequence is [tex]\( 79 \)[/tex].
### Final Result:
The first five numbers in the sequence are:
[tex]\[
99, 94, 89, 84, 79
\][/tex]
Hence, the first five numbers generated by the sequence [tex]\( f(n) = 99 - 5(n-1) \)[/tex] are [tex]\( 99, 94, 89, 84, 79 \)[/tex].
