14. Sequences & Series

The first 4 terms of a sequence are $\(\left\[\lbrace\]\sqrt\)3,2\(\sqrt\)3,3\(\sqrt\)3,4\(\sqrt\)3,\(\ldots\[\right\]\rbrace\)$. Continuing this pattern, find the $7^{\(\th\)}$ term.

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\(\frac{1}{n!+1}\)$

Write a recursive formula for the arithmetic sequence.

$\(\left\]\lbrace\)8,2,-4,-10,\(\ldots\[\right\]\rbrace\)$

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\(\th\)}$ term.

$\(\left\]\lbrace\)-9,-4,1,6,\(\ldots\[\right\]\rbrace\)$