Complete the string with the missing number 2,8,14,20,x,32.

Expert Answers
justaguide eNotes educator| Certified Educator

We have the series 2, 8, 14, 20, x, 32.

If we have a look at the terms we see that 8 - 2 = 14 - 8 = 20 - 14 = 6.

Therefore the series is an arithmetic progression with the common difference 6.

So x - 20 = 6

=> x = 26

Again, as verification we see  that 32 - 26 = 6.

The missing term x is equal to 26.

judibeefl | Student

This is a pattern sequence question. Look at the numbers we have been given:

2,8,14,20, X, 32

X is the number missing in the pattern sequence. Look at the other given numbers; 2, 8, 14, 20. Do you see a number pattern here amongst these numbers? Look at the numbers 2 and 8. What is the number difference here between the numbers? To get to the number 8 from the number 2, how many spaces must we move. We are already on 2, so let us count over to 8, starting with the number 3 because we ae already on 2!   3, 4, 5, 6, 7, 8 How many spaces did we need to count over to get to the numbe 8?  6, that is correct!  Now let's do the same steps for the numbers between 8 and 14; ready; 9,10,11,12,13,14. How many spaces did we need to get to 14?   6.   Do you see a number sequence pattern now? If so, you should be able to find out what X is by adding the pattern number we just discovered! Are you still not sure? Let's take the numbers 14 and 20, and apply the same steps; ready?  15, 16,17,18,19,20. How many spaces did we need to get to 20?  6!  Hmm that number 6 seems to have come 3 times now!  Let us see what happens if we count over 6 spaces from here; ready?  21,22,23,24,25,26. Great, now let us take the last number, and count back 6 numbers and see what number that brings us too, resdy?  31,30,29,28,27,26. Hmm there is that number 26 again. Let us bring the original question back:

2,8,14,20, X, 32 What number logically could and will replace the letter X?  26?  Great, because 26 is your answer!

To answer these in the future, remember it is best find the pattern first, and this will help you solve the answer!

giorgiana1976 | Student

We notice that each term from the given series could be obtained by adding the constant amount 6 to the previous term.

Let's start with the 2nd term 7:

8 = 2 + 6

14 = 8 + 6

20 = 14 + 6

This tells us that "x" is the following term in the given string, that can be obtained by adding the constant amount 6, to the previous term 20.

x = 20 + 6

x = 26

The given string is an arithmetic series, whose common difference is d = 6.

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