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Question
Sachin invested in a national saving certificate scheme. In the first year he invested Rs 5000 , in the second year Rs 7000, in the third year Rs 9000 and so on. Find the total amount that he invested in 12 years.
Solution
Sachin invested in first year = Rs 5000
Second year investment = Rs 7000
Third year investment = Rs 9000
Total investment = Rs (5000 + 7000 + 9000 + ..... + in 12 years)
Here,
a = 5000
d = 2000
n = 12
Now,
\[S_n = \frac{n}{2}\left( 2a + \left( n - 1 \right)d \right)\]
\[ S_{12} = \frac{12}{2}\left( 2a + \left( 12 - 1 \right)d \right)\]
\[ = \frac{12}{2}\left( 2\left( 5000 \right) + \left( 12 - 1 \right)\left( 2000 \right) \right)\]
\[ = 6\left( 10000 + 22000 \right)\]
\[ = 6\left( 32000 \right)\]
\[ = 192000\]
Hence, the total amount that he invested in 12 years is Rs 192000.
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