**Question:**

A man accepts a position with an initial salary of ₹26000 per month. It is understood that he will receive an automatic increase of ₹250 in the very next month and each month thereafter.

Find this

(i) salary for the 10th month,

(ii) total earnings during the first year

**Solution:**

Given: -

An initial salary that will be given = ₹26000

There will be an automatic increase of ₹250 per month from the very next month and thereafter.

Hint: - In the given information the salaries he receives are in A.P.

Let the number of the month is $\mathrm{n}$.

Initial salary $=a=₹ 26000$

Increase in salary $=$ common difference $=d=₹ 250$

i. Salary for the $10^{\text {th }}$ month,

n = 10,

Salary = a + (n - 1)×d

$=26000+(10-1) \times 250$

$=28250$

∴ Salary for the 10th month = ₹28250

ii. Total earnings during the first year = sum off all salaries received per month.

Total earnings $=\frac{n}{2}[2 \times a+(n-1) \times \mathrm{d}]$

Here n = 12

Total earnings $=\frac{12}{2}[2 \times 26000+(12-1) \times 250]$

$=6 \times(42000+2750)$

$=268500$

Total earnings during the first year = ₹268500