the amount of interest earned on an account can be represented using the recursive formula a_n = 1.02(a_n…

the amount of interest earned on an account can be represented using the recursive formula a_n = 1.02(a_n - 1). if a_1 = 255.00, and n represents the number of months the money is invested, what is the balance at the end of each month for the first three months? $255.00, $260.10, $265.30 $255.00, $260.10, $265.20 $255.00, $256.02, $257.04 $255.00, $250.00, $245.10

the amount of interest earned on an account can be represented using the recursive formula a_n = 1.02(a_n - 1). if a_1 = 255.00, and n represents the number of months the money is invested, what is the balance at the end of each month for the first three months? $255.00, $260.10, $265.30 $255.00, $260.10, $265.20 $255.00, $256.02, $257.04 $255.00, $250.00, $245.10

Answer

Explanation:

Step1: Find balance for month 1

Given $a_1 = 255.00$, so the balance at the end of the first - month is $a_1=$255.00$.

Step2: Find balance for month 2

Use the recursive formula $a_n = 1.02(a_{n - 1})$. When $n = 2$, $a_2=1.02\times a_1$. Substitute $a_1 = 255.00$ into the formula: $a_2=1.02\times255.00 = 260.10$.

Step3: Find balance for month 3

When $n = 3$, $a_3=1.02\times a_2$. Substitute $a_2 = 260.10$ into the formula: $a_3=1.02\times260.10=265.302\approx265.30$.

Answer:

$255.00, $260.10, $265.30