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Home » 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?
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?
CBSE | Class 11 | Maths | NCERT Exemplar | Sequences and Series
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?

Solution:

It is given that the total amount saved is 66000 in 20 years, therefore {{S}_{20}}~=\text{ }66000

Let ‘a’ be the amount saved in first year.

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

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

The sequence so formed is an AP and their common difference therefore is d = 200

As he saved money for 20 years therefore there are 20 terms in the sequence.

By using the formula for AP {{S}_{n~}}=\text{ }n/2\text{ }\left( 2a\text{ }+\text{ }\left( n\text{ }\text{-}1 \right)\text{ }d \right) we obtain

Where the number of terms is ‘n’ and the first term is ‘a’ and the common difference is ‘d’ Given that

\begin{array}{*{35}{l}} \Rightarrow ~6600\text{ }=\text{ }2a\text{ }+\text{ }3800 \\ \Rightarrow ~6600{-}3800\text{ }=\text{ }2a \\ \Rightarrow ~2a\text{ }=\text{ }2800 \\ \Rightarrow ~a\text{ }=\text{ }1400 \\ \end{array}

As a result, Rs.1400 is the amount saved in first year.

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