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.
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.

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 n.
Initial salary = a = ₹26000
Increase in salary = common difference = d = ₹250
i. Salary for the 10th month,
n = 10,
Salary = a + (n – 1)×d
= 26000 + (10 – 1)×250
= 28250
∴ Salary for the 10th month = ₹28250
ii. Total earnings during the first year = sum off all salaries received per month.

Total earnings =

$\frac{n}{2}\left[2a+\left(n–1\right)d\right]$

Here n = 12.

Total earnings=

$\frac{12}{2}\left[2×26000+11×250\right]$

= 6×(42000 + 2750)
= 268500
Total earnings during the first year = ₹268500