**Question:**

A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the preceding year. How much did he save in the first year?

**Solution:**

Here, we are given that the total saving of a man is Rs 16500 and every year he saved Rs 100 more than the previous year.

So, let us take the first installment as *a.*

Second installment =

Third installment =

So, these installments will form an A.P. with the common difference (*d*) = 100

The sum of his savings every year

Number of years (*n*) = 10

So, to find the first installment, we use the following formula for the sum of *n* terms of an A.P.,

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

Where; *a* = first term for the given A.P.

*d* = common difference of the given A.P.

*n *= number of terms

So, using the formula for *n* = 10, we get,

$S_{10}=\frac{10}{2}[2(a)+(10-1)(100)]$

$16500=5[2 a+(9)(100)]$

$16500=10 a+4500$

$16500-4500=10 a$

Further solving for *a,*

*$10 a=12000$*

$a=R s 1200$

Therefore, man saved ${R s} 1200$ in the first year.