Question

The recursive formula for a sequence is shown.

a1=−29

an=an−1+13

Which function produces the same sequence?

Responses

f(n)=−42+13n
f ( n ) = − 42 + 13 n

f(n)=−29+13n
f ( n ) = − 29 + 13 n

f(n)=−42n+13
f ( n ) = − 42 n + 13

f(n)=−29n+13

Answer 1

The correct function that represents the given recursive sequence is f(n) = -42 + 13n. therefore correct option is A

Step-by-step explanation:

The recursive formula given for a sequence is an = an-1 + 13 with the initial value a1 = −29.

To find the explicit function that produces the same sequence, we need to find a function f(n) that gives the value of the nth term directly.

Given the sequence's recursive nature, we add 13 n times to the initial value, but we subtract one instance of 13 because the initial value already includes the first term's value.

This yields f(n) = −29 + 13(n-1).

Simplifying this we get f(n) = −29 + 13n - 13 which further simplifies to f(n) = −42 + 13n.

Therefore, the correct function is f(n) = −42 + 13n.