A person saves each year Rs 100 more than he saved in the

This is an evenly spaced set.

For evenly spaced set you can apply the formula to find the sum, which is:
\(\frac{(First Term + Last Term)}{2}\) times the Total Number of terms.


Let n be the total number of terms (or total no. of years for this question)
As we don't have the last term we'll have to make do with this as the last term: \((n-1)*100+200\) (as every term increase by 100 from the preceding one, and the first term is 200. Take note that n is also the last term)

Algebra equation:
\(23000=n*\frac{200+[(n-1)*100+200]}{2}\)
\(23000=n*\frac{200+(100n-100+200)}{2}\)
.....
end up with this
\(n^2+3n-460=0\) (could have used the answer choices to test which one fits)
\((n+23)(n-20)=0\)

\(n={-23,20}\)

As n cannot be negative, so the answer is 20.