A man saved Rs 66000 in 20 years.

Given the total amount saved in 20 years is 66000 hence S20 = 66000

Let the amount saved in first year be ‘a’

Then as he increases 200 Rs every year then the amount in second year will be ‘a + 200’ then in third year ‘a + 400’ and so on

The sequence will be a, a + 200, a + 400…

The sequence is AP and the common difference is d = 200

There are 20 terms in the sequence as he saved money for 20 years

Using the sum formula for AP Sn = n/2 (2a + (n – 1) d) we get

Where n is number of terms a is the first term and d is the common difference

Given that S20 = 66000

S20 = (20/2) (2a + (20 – 1) 200)

⇒ 66000 = 10(2a + 19 × 200)

⇒ 6600 = 2a + 3800

⇒ 6600 – 3800 = 2a

⇒ 2a = 2800

⇒ a = 1400

Hence amount saved in first year is 1400 Rs.