Answer:
![a_n = a_{n-1} (1.06) + 50](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D%20%281.06%29%20%2B%2050)
Step-by-step explanation:
Suppose,
is initial amount in the saving account,
Here, the annual interest rate is 6% and additional amount in each year is $ 50,
So, the amount after one year,
![a_1 = a_0 + 6\%\text{ of }a_0 + 50 = a_0 + 0.06a_0 + 50 = a_0(1.06) + 50](https://tex.z-dn.net/?f=a_1%20%3D%20a_0%20%2B%206%5C%25%5Ctext%7B%20of%20%7Da_0%20%2B%2050%20%3D%20a_0%20%2B%200.06a_0%20%2B%2050%20%3D%20a_0%281.06%29%20%2B%2050)
Amount after 2 years,
![a_2 = a_1 + 6\%\text{ of }a_1 + 50 = a_1(1.06) + 50](https://tex.z-dn.net/?f=a_2%20%3D%20a_1%20%2B%206%5C%25%5Ctext%7B%20of%20%7Da_1%20%2B%2050%20%3D%20a_1%281.06%29%20%2B%2050)
Amount after 3 years,
![a_3 = a_2 + 6\%\text{ of }a_2 + 50 = a_2(1.06) + 50](https://tex.z-dn.net/?f=a_3%20%3D%20a_2%20%2B%206%5C%25%5Ctext%7B%20of%20%7Da_2%20%2B%2050%20%3D%20a_2%281.06%29%20%2B%2050)
................................., so on....
Hence, by following the pattern,
The amount after n years,
![a_n = a_{n-1} (1.06) + 50](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D%20%281.06%29%20%2B%2050)
Which is the required recurrence relation for the amount of money in a savings account