A teacher earns $\$x$ in his first year and his salary increases each year by 10% of his first year's salary. His total salary after $n$ years is

\dfrac{nx(n+19)}{20}

\dfrac{nx(n+9)}{10}

x(1.1)^{n}

\dfrac{nx(n-1)}{20}

Explanation: The salaries form an AP with first term

x

and common difference

0.1x

, so

S_n=\tfrac{n}{2}[2x+(n-1)(0.1x)]=\tfrac{nx}{2}\cdot\tfrac{19+n}{10}=\tfrac{nx(n+19)}{20}

Derived from ZIMSEC Mathematics Paper 1, June 2011, Q12

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