## Thinking Mathematically (6th Edition)

Case 1: Company A Starting salary is$\20,000$. Increment per year is$\1000$. So, the salary year by year is; $\20000,\21000,\22000,\23000,\ldots$ It is a form of A.P. Where $a=\20000$and the common difference $d=\1000$ It is known that the nth term in A.P is; ${{a}_{n}}=a+\left( n-1 \right)d$ And, \begin{align} & {{a}_{7}}=20000+\left( 6-1 \right)1000 \\ & =20000+5\times 1000 \\ & =20000+5000 \\ & =25000 \end{align} Case 2: Company B Starting salary is$\20,000$. Increment per year $5%$ of salary; $\frac{5}{100}\times 20000=1000$ So, the salary of the starting of second year is $21000$. Salary of the staring of third year is; \begin{align} & 21000+\left( \frac{5}{100}\times 21000 \right)=21000+1050 \\ & =22050 \end{align} Salary of the staring of fourth year is; \begin{align} & 22050+\left( \frac{5}{100}\times 22050 \right)=22050+1102.5 \\ & =23152.5 \end{align} Salary of the staring of fifth year is; \begin{align} & 23152.5+\left( \frac{5}{100}\times 23152.5 \right)=23152.5+1157.6 \\ & =24310.1 \end{align} Salary of the staring of sixth year is; \begin{align} & 24310.1+\left( \frac{5}{100}\times 24310.1 \right)=24310.1+1215.5 \\ & =25525.60 \end{align} Hence, the company B pay more as compare to company A.