A man saved ₹ 16500/- in ten years . in each year after the first he saved ₹ 100/- more then he did in the preceding year. How much did he saved in the first year?
Given: A man saved 16500/- in ten years
To find: His saving in the first year
Let he saved Rs. x in the first year
Since each year after the first he saved 100/- more then he did in the preceding year
So,
A.P will be x, 100 + x, 200 + x………………..
where x is first term and
common difference, d = 100 + x – x = 100
We know,
Sn is the sum of n terms of an A.P
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
According to the question:
Sn = 16500 and n = 10
Therefore,
⇒ 16500 = 5{2x + 9(100)}
⇒ 16500 = 5(2x + 900)
⇒ 16500 = 10x + 4500
⇒ -10x = 4500 – 16500
⇒ –10x = –12000
⇒ x = 1200
Hence, his saving in first year is 1200