First slide

Arithmetic progression

Question

A man saved Rs 66000 in 20 yr. 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?

Moderate

A

Rs.1450
B

Rs.1400
C

Rs.1470
D

Rs.1480

Solution

Here, $n = 20, S_{n} = 66000, d = 200$
Let first term is a
$\begin{array}{l} ∵ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ ∴ 66000 = \frac{20}{2} [2 \times a + (20 - 1) 200] \\ \Rightarrow 6600 = 2 a + 19 \times 200 \\ \Rightarrow 2 a = 6600 - 3800 \\ \Rightarrow 2 a = 2800 \\ \Rightarrow a = 1400 \end{array}$
Hence, he save in the first year is Rs1400.

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