Question

Find the 133rd term in the sequence: -7, -2, 3, 8

Answer 1

There is a common difference between terms of 5, which means the sequence is given recursively by

$\begin{cases}a_1=-7\\a_n=a_{n-1}+5&\text{for }n>1\end{cases}$

and explicitly by

$a_n=-7+5(n-1)=5n-12$

This means the 133rd term in the sequence is $a_{133}=5(133)-12=653$