Sure! Let's find the largest number in the given sequence, which is described by the formula [tex]\( 60 - 8n \)[/tex].
1. Understand the formula: The formula given is [tex]\( 60 - 8n \)[/tex], where [tex]\( n \)[/tex] represents the term number in the sequence.
2. Identify the behavior of the sequence: The sequence is decreasing because the term [tex]\( -8n \)[/tex] will become more negative as [tex]\( n \)[/tex] increases. Hence, the larger the [tex]\( n \)[/tex], the smaller the term value.
3. Determine the value of [tex]\( n \)[/tex] that gives the largest term: Since the sequence decreases as [tex]\( n \)[/tex] increases, the largest term will be when [tex]\( n \)[/tex] is the smallest possible value. Generally, in sequences, [tex]\( n \)[/tex] starts from 0.
4. Substitute [tex]\( n = 0 \)[/tex] into the formula:
[tex]\[
\text{term} = 60 - 8 \times 0
\][/tex]
Simplifying this, we get:
[tex]\[
\text{term} = 60 - 0 = 60
\][/tex]
Hence, the largest number in the sequence [tex]\( 60 - 8n \)[/tex] is [tex]\( 60 \)[/tex].
