Question

b-118. write a recursive equation for the sequence graphed at the right.

Explanation:

Step1: Identify sequence terms

From the graph: $t(1)=6$, $t(2)=18$, $t(3)=54$

Step2: Find common ratio

Calculate $\frac{t(2)}{t(1)}=\frac{18}{6}=3$, $\frac{t(3)}{t(2)}=\frac{54}{18}=3$

Step3: Write recursive formula

Recursive form for geometric sequence: $t(n) = 3 \cdot t(n-1)$ with initial term $t(1)=6$, for $n\geq2$

Answer:

$t(1) = 6$, $t(n) = 3t(n-1)$ for $n \geq 2$