Question

1. consider the sequence whose first four terms are 20, 17, 14, 11. write a function, f(n), that can be used to define this sequence. (hint: will it be an arithmetic/linear or geometric/exponential?)

Explanation:

Step1: Identify sequence type

Check difference: $17-20=-3$, $14-17=-3$, $11-14=-3$ → arithmetic.

Step2: Use arithmetic formula

Formula: $f(n)=a_1+(n-1)d$, $a_1=20$, $d=-3$.

Step3: Simplify the formula

$f(n)=20+(n-1)(-3)=20-3n+3=-3n+23$.

Answer:

$f(n) = -3n + 23$