Question

Write the explicit equation for the sequence 5,8,11,14

Answer 1

Consecutive terms differ by 3, so

$a_n=a_{n-1}+3=a_{n-2}+2\times3=a_{n-3}+3\times3=\cdots=a_1+(n-1)\times3$

Since the first term is $a_1=5$, the formula for the sequence is

$a_n=5+3(n-1)=3n+2$