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.

Answer 1

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,
$$\begin{gathered} S_n=\frac{n}{2}\left(2a+\left(n-1\right)d\right) \\ {S}_{12}=\frac{12}{2}\left(2a+\left(12-1\right)d\right) \\ =\frac{12}{2}\left(2\left(5000\right)+\left(12-1\right)\left(2000\right)\right) \\ =6\left(10000+22000\right) \\ =6\left(32000\right) \\ =192000 \end{gathered}$$

Hence, the total amount that he invested in 12 years is Rs 192000.