Question

exit ticket
write a recursive equation and explicit equation
for this pattern:
the first term in this arithmetic sequence is 2.
the next term is 5 and the pattern continues by
adding three to get each of the remaining terms.

Explanation:

Step1: Define recursive base case

The first term $a_1 = 2$

Step2: Define recursive recurrence relation

For $n \geq 2$, each term is prior term +3:
$a_n = a_{n-1} + 3$

Step3: Identify explicit formula components

Arithmetic sequence form: $a_n = a_1 + (n-1)d$, where $a_1=2$, $d=3$

Step4: Substitute values into explicit formula

$a_n = 2 + (n-1) \times 3$
Simplify: $a_n = 3n - 1$

Answer:

Recursive equation:
$a_1 = 2$
$a_n = a_{n-1} + 3$ for $n \geq 2$

Explicit equation:
$a_n = 3n - 1$