# Algebra Quiz

## Make sure to try these on a piece of paper first

In an arithmetic sequence, the first term is 2, and the fourth term is 14.

a) Find the common difference, d.

b) Calculate the sum of the first 14 terms, $latex S_{14}$.

Let $latex log_{b}\, 2=u$, and $latex log_{b}\, 5=v$. Find an expression in terms of u and v for:

a) $latex log_{b}\, 10$.

b) $latex log_{b}\, 25$.

Find the $latex x^{3}$ term in the expansion of $latex \left ( x-\frac{2}{x} \right )^{5}$.

The first 3 terms in a geometric sequence are: $latex k^{2}, \: -k, \: k-2$.

a) Find the value of k.

b) Find the sum of the terms to infinity.

In an arithmetic series, $latex S_{20}=670$, and $latex u_{20}=62$.

a) What is the first term, $latex u_{1}$?

b) What is the common difference, d?

Solve the following sum:

$latex \sum_{n=1}^{100}2n+3$

Simplify $latex \frac{\left (-6 x^{-2}y^{2} \right ) \left (-8x^{-5}y^{-3} \right )}{4x^{2}y^{-4}}$.

The sum of the first 6 terms of a sequence is 39.75. Also, the 7^{th} term is $latex \frac{6}{5}$ times the 2^{nd} term. Find the first term and the common difference of the sequence.

Let $latex log_{8}A=x, \, log_{8}B=y, \, log_{8}C=z$. Express $latex log_{8}\left ( \frac{A^{2}}{B^{3}C} \right )^{4}$ in terms of x, y and z.

Consider the expansion of $latex \left ( \frac{1}{3}x – 2 \right ) ^{7}$. Find the coefficient of $latex x^{3}$.