Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

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Solving for a geometric series

Solving for a geometric series

Solving for a geometric series

Find the sum of the first n terms of a Geometric progression

Find the nth term of a Geometric progression

Find the sum of the first n terms of an arithmetic progression

Find the nth term of an Arithmetic progression

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Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Simplify logarithmic expressions using rules on logarithms.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Recognising the equation of a circle.