Answered

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A sequence is defined recursively by the formula [tex][tex]$f(n+1) = f(n) + 3$[/tex][/tex]. The first term of the sequence is -4. What is the next term in the sequence?

A. -7
B. -1
C. 1
D. 7

Sagot :

GinnyAnswer
To find the next term in the sequence, let's analyze the given information and use the recursive formula provided.

The sequence is defined by:
[tex]\[ f(n+1) = f(n) + 3 \][/tex]

And we know that the first term of the sequence is:
[tex]\[ f(1) = -4 \][/tex]

We need to find the second term of the sequence, which is [tex]\( f(2) \)[/tex].

According to the recursive definition:
[tex]\[ f(n+1) = f(n) + 3 \][/tex]

By substituting [tex]\( n = 1 \)[/tex]:
[tex]\[ f(2) = f(1) + 3 \][/tex]

We already know [tex]\( f(1) = -4 \)[/tex]:
[tex]\[ f(2) = -4 + 3 \][/tex]

Finally, performing the addition:
[tex]\[ f(2) = -1 \][/tex]

Therefore, the next term in the sequence is:
[tex]\[ \boxed{-1} \][/tex]
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