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A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
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.