Question

What are the next three terms in the sequence 5, 14, 23, 32, ...? 43, 54, 65 45, 54, 63 41, 50, 59 47, 56, 65

Answer 1

Hello!

If we just look at the last digit, we see 5, 4, 3, 2, 1. This means that it most likely has something minus one. If we look at the tens place, we see 0, 10,20, 30. Here we see +10. Therefore our pattern is x+10-1. 10-1=9. Our pattern now is x+9.

To find the next three terms, let's start by having 32 equal x, and then switch the answer to the expression to x and repeat.
32+9=41
41+9=50
50+9=59

Our next three values are 41, 50, and 59.

I hope this helps!

Answer 2

Take a careful look at 5, 14, 23, 32. Each new term is equal to the previous term PLUS 9. Thus, 9 is the "common difference."

Next 3 terms?

32 plus 9 is 41
41 plus 9 is 50
50 plus 9 is 59
59 plus 9 is 68.
and so on

So the "next 3 terms in the seq. 5, 14, 23, 32 are 41, 50, 59.