The first number of the sequence is 3 and the fifth number is 31 how do I find the numbers in between?

Answer 1

There are two basic types of sequences, arithmetic (where you add a number to get to the next term of the sequence) or geometric (where you add a number to get to the next term of the sequence). You first need to know which type of sequence this is. For reasons I'll discuss later, I'm guessing this is an arithmetic sequence.

If we map out the sequence, it would look like this:

So I'm taking some number, let's call it "x", and adding it to 3, then adding it to the 2nd term, then adding it to the third term, then adding it to the 4th term and getting 31 as the answer. I can write that like this:

3 + x + x + x + x = 31 or

3 + 4x = 31 then subtracting 3 from both sides:

4x = 28 then dividing by 4:

x = 7

So the 2nd term is 10 (because 3 + 7 = 10), the third is 17 (because (10 + 7 = 17), and the 4th is 24 (because 17 + 7 = 24). Notice that if we add 7 to the 4th term (24), we get 31, our given 5th term.

If this were a geometric sequence, it would still be possible to compute the values of terms 2, 3, and 4 but it doesn't turn out to be a nice even number in this case. To do so we would have:

3*x*x*x*x = 31 or

3x⁴ = 31

x⁴ = 31/3

x = the 4th root of 31/3 which is a complicated number and probably not what this problem is about. To get each term, we would multiply by the 4th root of 31/3 to get the next term number.

Answer 2

Assuming that this is an Arithmetic Sequence that grows by adding the same number, I will show you two methods that you can figure it out.

Method 1: Guess and Check - Start with 3 and guess a number that you have to add each time to end at a 5th number of 31.

Adding by 2: 3, 5, 7, 9, 11 (Not big enough)

Adding by 5: 3, 8, 13, 18, 23 (Still not big enough)

Adding by 7: 3, 10, 17, 24, 31 (Since 31 is the 5th number, this is the correct answer)

Method 2: Subtract and Divide

3 — — — 31

31 - 3 = 28

You need to add the same number 4 times to the 1st number to end at the 5th number. What is this number? Four of what number will add to 28?

28 ÷ 4 = 7

Adding by 7, you can complete the sequence.

3, 10, 17, 24, 31

Answer 3

doing the problem as a geometric sequence gave an irrational number for the common ratio

I'm assuming that it is an arithmetic sequence

a_n=a₁+(n-1)d

31=3+(5-1)d

31=3+4d

28=4d

d=7, the common difference

3, 10, 17, 24, 31