Question

The amount of money in Nadia’s savings account is represented by the recursive formula an=1.025(an-1)+50 if a6=291.51 what are the first two numbers in the sequence?

A. $25.36, $75.99
B. $50.00, $101.25
C. $101.25, $153.78
D. $75.99, $127.89

Answer 1

The answer is A. I just took the test

Answer 2

Answer: A. $25.36, $75.99

Explanation:

Given recursive formula:
`a_n=1.025(a_(n-1))+50`

Also,
`a_6=291.51`

Put n=6 in the above formula , we get

`a_6=1.025(a_(6-1))+50\\\Rightarrow291.51=1.025(a_5)+50\\\Rightarrow1.025(a_5)=291.51-50\\\Rightarrow1.025(a_5)=241.51\\\Rightarrow(a_5)=235.619512195`

Similarly, for n=5 in the above formula , we get

`a_5=1.025(a_(5-1))+50\\\Rightarrow235.619512195=1.025(a_4)+50\\\Rightarrow1.025(a_4)=235.619512195-50\\\Rightarrow1.025(a_4)=185.619512195\\\Rightarrow(a_4)=181.09220702`

for n=4 in the above formula , we get

`a_4=1.025(a_(4-1))+50\\\Rightarrow181.09220702=1.025(a_3)+50\\\Rightarrow1.025(a_3)=181.09220702-50\\\Rightarrow1.025(a_3)=131.09220702\\\Rightarrow(a_3)=127.894836117`

for n=3 in the above formula , we get

`a_3=1.025(a_(3-1))+50\\\Rightarrow127.894836117=1.025(a_2)+50\\\Rightarrow1.025(a_2)=127.894836117-50\\\Rightarrow1.025(a_2)=77.894836117\\\Rightarrow(a_2)=75.9949620654\approx75.99`

for n=2 in the above formula , we get

`a_2=1.025(a_(2-1))+50\\\Rightarrow75.99=1.025(a_1)+50\\\Rightarrow1.025(a_1)=75.99-50\\\Rightarrow1.025(a_1)=25.99\\\Rightarrow(a_1)=25.356097561\approx25.36`

Hence, the first two numbers in the sequence are $25.36 and $75.99.