Question

Ram invests a total sum of 2000 rupees on government bonds in 4 years. If these investments are in A.P and the sum of squares of the investments is 1200000. Find the investment made by ram in each year respectively. It is also known that he always invests more than the previous year.

Answer 1

take the numbers as  

(a-3d),(a-d),(a+d),(a+3d)

So, Let the investment made by Ram in these years be (a-3d),(a-d),(a+d),(a+3d)

Then,

(a-3d) + (a-d) + (a+d) +(a+3d) = 2000

=> 4a = 2000

=> a = 500

Now, again AQ

(a-3d)^2 +(a-d)^2 +(a+d)^2 +(a+3d)^2 = 1200000

=> 4(a2 + 5 d^2) = 1200000

=> (a2 + 5 d^2) = 300000

=> 250000 + 5d^2 = 300000

=> 5d^2 = 50000

=> d^2 = 10000

=> d = ±100

∴ d = 100 ( As the investment increases every year so d = -100 not possible)

Hence the investments made are 200,400,600,800

Hope this helps!