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atroni [7]
3 years ago
5

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 t

he 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
Mathematics
2 answers:
Alexus [3.1K]3 years ago
7 0
The answer is A. I just took the test
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nataly862011 [7]3 years ago
5 0

Answer: A. $25.36, $75.99

Step-by-step 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.

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Answer:

Al estudiante le falta caminar \frac{1}{3} de kilómetro.

Step-by-step explanation:

Un estudiante debe recorrer dos tercios de kilómetro para llegar al colegio. Dos tercios equivale a la fracción \frac{2}{3} .

El estudiante avanza medio kilómetro en bus. Un medio equivale a la fracción \frac{1}{2}, por lo tanto un medio es la mitad de una cantidad.  Para calcular la distancia recorrida en bus se realiza la siguiente multiplicación:

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Resolviendo:

\frac{1}{2} *\frac{2}{3} =\frac{1*2}{2*3} =\frac{2}{6} =\frac{1}{3}

Entonces, la distancia recorrida en bus es \frac{1}{3} de kilómetro.

Para calcular la distancia recorrida a pie se calcula la diferencia entre la distancia total a recorrer por el estudiante y la distancia recorrida en bus. Esto es:

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Resolviendo:

\frac{2}{3} - \frac{1}{3}=\frac{2-1}{3} =\frac{1}{3}

<u><em>Al estudiante le falta caminar </em></u>\frac{1}{3}<u><em> de kilómetro.</em></u>

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