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A sequence is defined recursively using the equation [tex]f(n+1) = f(n) - 8[/tex]. If [tex]f(1) = 100[/tex], what is [tex]f(6)[/tex]?

A. 52
B. 60
C. 68
D. 92

Sagot :

GinnyAnsweridn
To find [tex]\( f(6) \)[/tex] in the given sequence defined recursively by [tex]\( f(n+1) = f(n) - 8 \)[/tex] with the initial value [tex]\( f(1) = 100 \)[/tex], follow these steps:

1. Start with the initial value:
[tex]\[ f(1) = 100 \][/tex]

2. Use the recurrence relation to find the subsequent terms:
[tex]\[ f(2) = f(1) - 8 = 100 - 8 = 92 \][/tex]
[tex]\[ f(3) = f(2) - 8 = 92 - 8 = 84 \][/tex]
[tex]\[ f(4) = f(3) - 8 = 84 - 8 = 76 \][/tex]
[tex]\[ f(5) = f(4) - 8 = 76 - 8 = 68 \][/tex]
[tex]\[ f(6) = f(5) - 8 = 68 - 8 = 60 \][/tex]

So, the value of [tex]\( f(6) \)[/tex] is [tex]\( 60 \)[/tex].

Thus, the correct answer is 60.
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