A man saved Rs. 16,500 in 10 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?

A man saved Rs. 16,500 in 10 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:
Let us assume that the amount the man saved in the  first year=a
Here S=16,500
          n=10
          d=100
We are to find the value of a.
We know,
Sₙ= (n/2)*{2a+(n-1)*d}
⇒16,500=(10/2)*{2a+(10-1)*100}
⇒16,500=5*{2a+9*100}
⇒16,500/5=2a+900
⇒3300=2a+900
⇒3300-900=2a
⇒2400=2a
⇒2400/2=a
⇒1200=a
⇒a=1200.
Therefore the man saved in the first year=Rs. 1200