Weird n stuff: for a0=1 and an+1 = 2an+1 for n=0,1,2,… What is the value of a4?

[Batarang96]

Weird n stuff: for a0=1 and an+1 = 2an+1 for n=0,1,2,… What is the value of a4?

I have no idea where to start, here. I'm reviewing for the accuplacer test, and I'm just not able to comprehend the examples I've been looking at.

The sequence a_n is defined by a₀=1 and a_n+1 = 2a_n+1 for n=0,1,2,… What is the value of a4?

 

[Deleted member 4993]

I have no idea where to start, here. I'm reviewing for the accuplacer test, and I'm just not able to comprehend the examples I've been looking at.

The sequence a_n is defined by a₀=1 and a_n+1 = 2a_n+1 for n=0,1,2,… What is the value of a4?

Is that correct?!

 

[Steven G]

Is that correct?!

Please look again as I think you have it wrong. Maybe it is a_n+1 = 2a_n + 1 ??

 

[Dr.Peterson]

I have no idea where to start, here. I'm reviewing for the accuplacer test, and I'm just not able to comprehend the examples I've been looking at.

The sequence a_n is defined by a₀=1 and a_n+1 = 2a_n+1 for n=0,1,2,… What is the value of a4?

I would assume it really said a_n+1 = 2a_n + 1, and asked for a₄. If it doesn't, then what I say will just be another example!

The idea here is that if you know one term in the sequence, a_n, then the formula tells you what the next one is, a_n+1.

You are told that a₀ = 1. So you can find a₁ by applying the formula with n = 0: a₀₊₁ = 2a₀ + 1 = 2(1) + 1 = 3. Then you can repeat to find a₂, then a₃, then a₄, which will be the answer.

Got it?

 

[Steven G]

I have no idea where to start, here. I'm reviewing for the accuplacer test, and I'm just not able to comprehend the examples I've been looking at.

The sequence a_n is defined by a₀=1 and a_n+1 = 2a_n+1 for n=0,1,2,… What is the value of a4?

If the rule is a_n+1 = 2a_n + 1, then this says to get the next term you multiply the proceeding term by 2 and then add 1. If you can say in words what the equation a_n+1 = 2a_n + 1 is saying then the rest is trivial.

 

[Batarang96]

I would assume it really said a_n+1 = 2a_n + 1, and asked for a₄. If it doesn't, then what I say will just be another example!

The idea here is that if you know one term in the sequence, a_n, then the formula tells you what the next one is, a_n+1.

You are told that a₀ = 1. So you can find a₁ by applying the formula with n = 0: a₀₊₁ = 2a₀ + 1 = 2(1) + 1 = 3. Then you can repeat to find a₂, then a₃, then a₄, which will be the answer.

Got it?

Thank you for the responses, everyone.

So a4 = 5, thus 2(5x3)+1 = 2(15)+1 = 31?