Question

A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?

Answer 1

We have,

the initial salary, a₁ = ₹5200,
the salary of the second month, a₂ = ₹5200 + ₹320 = ₹5520,
the salary of the third month, a₃ = ₹5520 + ₹320 = ₹5840,
.
.
.

$$\begin{gathered} \mathrm{As},a_2-a_1=5520-5200=320and{a}_3-a_2=5840-5520=320 \\ \mathrm{i}.\mathrm{e}.a_2-a_1=a_3-a_2 \\ \mathrm{So},a_1,a_2,a_3,...\mathrm{are}\mathrm{in}\mathrm{A}.\mathrm{P}. \\ \mathrm{Also},a=5200,d=320 \\ \left(\mathrm{i}\right)a_{10}=a+\left(10-1\right)d \\ =5200+9\times 320 \\ =5200+2880 \\ =8080 \\ \mathrm{So},\mathrm{the}\mathrm{salary}\mathrm{of}\mathrm{the}\mathrm{man}\mathrm{for}\mathrm{the}\mathrm{tenth}\mathrm{month}\mathrm{is}₹8,080. \\ \left(\mathrm{ii}\right)S_{12}=\frac{12}{2}\left[2a+\left(12-1\right)d\right] \\ =6\left(2\times 5200+11\times 320\right) \\ =6\left(10400+3520\right) \\ =6\times 13920 \\ =83520 \\ \mathrm{So},\mathrm{the}\mathrm{total}\mathrm{earnings}\mathrm{of}\mathrm{the}\mathrm{man}\mathrm{during}\mathrm{the}\mathrm{first}\mathrm{year}\mathrm{is}₹83,520. \end{gathered}$$