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# Sachin invested Rs. 5000 for first year, Rs. 7000 for the second year. Rs. 9000 in the third year in National Savings certificate scheme. How much amount did he invest 12 years ?

**Given :**

Amount invested by Sachin in first year $= Rs. 5000$

Amount invested by Sachin in second year $= Rs. 7000$

Amount invested by Sachin in third year $= Rs. 9000$

**To find :**

We have to find how much did sachin invest in 12 years.

**Solution :**

This implies, the sequence is,

5000,7000,9000,......

First term $= a = 5000$

common difference $= d = 7000-5000 = 2000$

The total amount that he invested in n = 12 years is,

Formula of sum of n terms in AP **$$\displaystyle S_{n} \ =\ \frac{n}{2} \ [ 2a\ +\ ( n-1) d]$$**

So total amount he invested in 12 years $= \frac{12}{2} [2\times5000+(12-1)\times2000]$

$= 6[10000+22000]$

$= 192000$

**The total amount invested by Sachin in 12 years is Rs. 1,92,000.**

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