3,6,9,15, 24,39 what is the next number in the sequence & why? i know it's going by 3 but its skipping numbers so I'm not sure if it would be 45,48,51,54,57,60,or 63

Ah, the delightful world of number sequences! Let me illuminate this for you.

Indeed, the pattern here is not as straightforward as it initially appears. Allow me to put on my clown hat and juggle some numbers for you.

If we look at the differences between consecutive terms, we can observe that they are: 3, 3, 6, 9, 15. Hmm, those numbers seem to be increasing themselves!

Now, let's focus on those differences. Can you see a pattern? Absolutely! If we continue this trend, the next difference would be 24 + 15 = 39.

Since our last term was 39, if we add the next difference of 39 to it, we get 39 + 39 = 78. So, according to this chuckle-worthy calculation, the next number in the sequence would be 78!

Of course, numbers can be quite cheeky sometimes, so be cautious. But hey, in the whimsical world of math, anything is possible.

To identify the pattern in the given sequence, let's look at the differences between consecutive terms:

6 - 3 = 3
9 - 6 = 3
15 - 9 = 6
24 - 15 = 9
39 - 24 = 15

From the differences, we can see that each subsequent difference is increasing by 3. This means that the differences between consecutive terms are in an arithmetic sequence: 3, 3, 6, 9, 15.

To find the next difference, we add 3 to the last difference:

15 + 3 = 18

Now, let's find the next number in the sequence by adding the difference to the last term:

39 + 18 = 57

Therefore, the next number in the sequence is 57.

To find the next number in the sequence, let's observe the pattern:

3, 6, 9, 15, 24, 39

If we look at the differences between consecutive terms, we get:

3, 3, 6, 9, 15

Now, let's examine the differences between these differences:

0, 3, 3, 6

We can see that the second set of differences is not constant, thus indicating that the sequence is not following a consistent pattern where a fixed number is being added/subtracted/multiplied. In this case, we can conclude that the sequence is not arithmetic or geometric.

However, if we focus on the first set of differences, we can notice that it is increasing by 3 each time:

3, 6, 9

Applying this pattern, we can determine the next difference by adding 3 to the last difference: 9 + 3 = 12.

Now, let's find the next number in the sequence by adding this difference to the last term:

39 + 12 = 51

Therefore, the next number in the sequence is 51.

In summary, the pattern in this sequence is that the differences between consecutive terms are increasing by 3 each time. By applying this pattern, we can determine that the next number in the sequence is 51.

Hint. Divide each number by 3 and the sequence should look familiar.