Question

34. Describe the arithmetic pattern, then give the next 3 terms in the sequence. 23, 31, 39, 47, …

Answer 1

First thing you must do when solving any math equation is read the question carefully taking note of all the numbers.

In this problem it is asking you to fish the arithmetic patters 23, 31, 39, 47.......

Usually to solve these kind of problems, you do the two first number minus each other:

23 - 31 = 8

Next, you would do the same with the next two numbers:

39 - 47 = 8

Now you can tell that there is a pattern going on here, for each number 8 is added.

So now we must to the math to find the next 3 numbers:

47 + 8 = 55

55 + 8 = 63

63 + 8 = 71

Thus, your three numbers 55, 63, and 71.

Just keep in mind that this way of solving does not work for all arithmetic patterns.

Hope this helped! :)

Answer 2

To find the common difference in this sequence when can use the formula:
`a_n-a_n_-_1`

This shows that we just need to subtract two number from the sequence in backwards order.

31 - 23 = 8

39 - 31 = 8

47 - 39 = 8

The common difference (rate) is 8.

To find the next 3 terms in the sequence we can add 8 to the last number in the sequence to find the next.

47 + 8 = 55 (5th term)

55 + 8 = 63 (6th term)

63 + 8 = 71 (7th term)

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Best Regards,

Wolfyy :)