Given,
Initial amount = Rs.90000
The amount given after every year = Rs. 30000
To Find,
The balance in the seventh year =?
In what year was the goal of Rs 420,000 met =?
Solution,
This is an AP as the common difference between each year is the same.
Therefore, a = Rs.90000 and d = Rs.30000
From the formula of the nth term in AP,
[tex]a_n = a +(n-1)d[/tex]
For the 7th year,
[tex]a_7 = 90000 +(7-1)30000\\a_7 = 90000 + 6*30000\\a_7 = 90000 + 180000\\a_7 = 270000[/tex]
For some value of n, the nth term is 420000
[tex]420000 = 90000 + (n-1)30000\\420000 - 90000 = (n-1)30000\\(n-1)*30000 = 330000\\n-1 = 330000/30000\\n-1 = 33/3\\n = 11 + 1\\n = 12[/tex]
Hence, the balance in the seventh year will be Rs. 270000 and after 12 years, the goal of Rs. 420000 was met.