Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 5, 11, 17, ... Find the 35th term.

Answer 1

175

1) Examining that Sequence we can find the common difference

11 -5 = 6

17 -11 = 6

First-term: 5

2) So, we can write out an Explicit Formula for that Arithmetic Sequence:

$\begin{gathered} a_n=a_1+(n-1)d \\ a_{35}=5\text{ +(34)}\times5 \\ a_{35}=5+170 \\ a_{35}=175 \end{gathered}$

3) Hence, the 35th term is 175