Question

Which sequence matches the recursive formula? an=2an-1+5, where a1=5. A) 5,10,15,20 B) 5,15,35,75. C)5,15,25,35. D) 5,20,35,40

Answer 1

The recursive formula

$a_n = 2a_{n-1}+5$

means that, to compute the next value, you have to double the previous one and then add 5.

So, we start with 5. To get the second term, we double it and add five, so we have

$a_2 = 2\cdot 5+5 = 10+5 = 15$

Next, we will double 15 and add 5:

$a_3 = 2\cdot 15 + 5 = 30+5 = 35$

So, the answer is B, because it's the only option starting with 5,15,35.

Just to check, let's compute the last step:

$a_4 = 2\cdot 35 + 5 = 70+5 = 75$

Which confirms option B