Which recursive formula was used to generate the first 5 terms of the sequence? 5, 10, 20, 40, 80

Question

Which recursive formula was used to generate the first 5 terms of the sequence?

5, 10, 20, 40, 80


an = 2an-1if a1= -5


an = 2an-1if a1= 5


an = an-1 + 2if a1= 5


an = 5an-1if a1= 2

Answer 1

Hi Alexis, the recursive formula, an = 2an_-1 if a₁ = 5, is the correct formula.

 

a₁ = 5

 

a₂ = 2 * a₁ or a₂ = 10

 

a₃ = 2 * a₂ or a₃ = 20

 

a₄ = 2 * a₃ or a₄ = 40

 

a₅ = 2 * a₄ or a₅ = 80

 

Questions?

Answer 2

A recursive formula defines each term in terms of the previous term. Poor English.

 

a_n = a_n-1(r)

 

a_n = a_n-1(2), if a₁ = 5

 

Second choice

Answer 3

Alexis,

For a recursive formula, each next value in a sequence will depend on a prior value. In this case, it's the exact value immediately prior to the next, 2a_n-1 means multiply 2 times a_n-1 where a is a sequence value and _n-1 tells where it's located. So if we look at the 3rd value in the sequence, 20... we got 20 by multiplying the 2nd value in the sequence, 10, by 2 (10 is immediately prior to 20 in the sequence), and if we look at the 5th value in this sequence, 80, we got 80 by multiplying the 4th value in the sequence, 40, by 2 (40 is immediately prior to 80 in the sequence)

 

So a_n = 2a_n-1 is our recursive formula but now we have to decide what a₁ is, which is actually asking what is the very 1st value given in our sequence?

 

Our first value in the given sequence is 5, so a₁ = 5.

 

Hope this helps!