14. Sequences & Series

The first 4 terms of a sequence are $\left\lbrace\sqrt3,2\sqrt3,3\sqrt3,4\sqrt3,\ldots\right\rbrace$. 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 the first 6 terms of the sequence given by the recursive formula $a_{n}=a_{n-2}+a_{n-1}$ ; $a_1=1$ ; $a_2=1$.

Write a recursive formula for the arithmetic sequence.

$\left\lbrace8,2,-4,-10,\ldots\right\rbrace$

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

$\left\lbrace-9,-4,1,6,\ldots\right\rbrace$

Write a recursive formula for the geometric sequence $\left\lbrace18,6,2,\frac23,\ldots\right\rbrace$.

Find the $10^{\th}$ term of the geometric sequence in which $a_1=5$ and $r=2$.

Write a formula for the general or $n^{\th}$ term of the geometric sequence where $a_7=1458$ and $r=-3$.