Question

Write a recursive formula for the sequence 7, 11, 15, 19, 23, ... then find the next term.

Answer 1

$\text{It's an arithmetic sequence:}\\\\a_1=7\\d=11-7=15-11=19-15=23-19=4\\\\\text{the formula of the nth term:}\\\\a_n=a_1+(n-1)d\\\\\text{substitute}\\\\a_n=7+(n-1)\cdot4=7+4n-4=4n+3\\\\\boxed{Answer:\ a_n=4n-3}$