Question

the pattern of numbers below is an arithmetic sequence:
14, 24, 34, 44, 54, ...
which statement describes the recursive function used to generate the sequence?
○ the common difference is 1, so the function is ( f(n + 1) = f(n) + 1 ) where ( f(1) = 14 ).
○ the common difference is 4, so the function is ( f(n + 1) = f(n) + 4 ) where ( f(1) = 10 ).
○ the common difference is 10, so the function is ( f(n + 1) = f(n) + 10 ) where ( f(1) = 14 ).
○ the common difference is 14, so the function is ( f(n + 1) = f(n) + 14 ) where ( f(1) = 10 ).

Explanation:

Step1: Find common difference

Calculate the difference between consecutive terms: $24-14=10$, $34-24=10$, $44-34=10$, $54-44=10$. The common difference is 10.

Step2: Identify initial term

The first term of the sequence is 14, so $f(1)=14$.

Step3: Match recursive formula

A recursive arithmetic sequence formula is $f(n+1)=f(n)+d$, where $d$ is the common difference. Substitute $d=10$ and $f(1)=14$.

Answer:

The common difference is 10, so the function is $f(n + 1) = f(n) + 10$ where $f(1) = 14$.