## Thinking Mathematically (6th Edition)

The salary for the sixth year will be$\38,288$.
In the first year, the salary of the player is \$30,000 and annual year the increment is 5%. So, \begin{align} & 5%\text{ of }30000=\frac{5}{100}\times 30000 \\ & =5\times 300 \\ & =1500 \end{align} So, the salary of the player at the starting of the second year is: $\30,000+\1,500=\31,500$ At the starting of the third year, the salary of the player will be again increased by 5%. \begin{align} & 5%\text{ of }31500=\frac{4}{100}\times 31500 \\ & =4\times 315 \\ & =1260 \end{align} The salary for the third year is: $\31,500+\1,260=\32,760$ Now the series is 30000, 31500, 32760……. It is a form of G.P The nth term is found in G.P with the help of the following formula ${{a}_{n}}=a{{r}^{\left( n-1 \right)}}$ The salary of the player accumulates according to G.P. with $a=30000,\,r=1\cdot 05$ and it is required to find ${{6}^{th}}$term. \begin{align} & {{a}_{n}}=a{{r}^{n-1}} \\ & {{a}_{6}}=30000\times {{\left( 1.05 \right)}^{\left( 6-1 \right)}} \\ & =30000\times {{\left( 1.05 \right)}^{5}} \\ & {{a}_{6}}=38288.44 \end{align} Hence, the salary in year 6 rounded off to the nearest dollar will be$\38,288$.