**9. Vijay invests some amount in National saving certificate. For the 1st year he invests Rs. 500, for the 2nd year he invests Rs. 700, for the 3rd year he invests Rs. 900, and so on. How much amount he has invested in 12 years ?**

**Sol. Yearly investments of Vijay are as follows 500, 700, 900, .......**

**The yearly investments form an A.P. with first year investment (a) = 500**

**Difference between investment done in two successive years (d) = 200.**

**No. of years (n) = 12**

**Total investment done in 12 years = (S12) = ?**

**Sn = n/2 [2a + (n – 1) d]**

**∴**

**S12 = 12/2[2 (500) + (12 – 1) 200]**

**∴**

**S12 = 6 [1000 + 11 (200)]**

**∴**

**S12 = 6 [1000 + 2200]**

**∴**

**S12 = 6 [3200]**

**∴**

**S12 = 19200**

**∴ Total investment done in 12 years is Rs. 19200.**