Question

10, 30, 90 continue the pattern

Answer 1

The answer is 270, the pattern is multiplying by 3. So, 10 • 3 = 30 30 • 3 = 90 90 • 3 = 270, and so on. Hope this helps! Let me know if you need any further assistant.

Answer 2

Answer:

• geometric sequence: 10, 30, 90, 270, 810, 2430, ...
• quadratic sequence: 10, 30, 90, 190, 330, 510, ...

Step-by-step explanation:

Three terms of a sequence can be the first three terms of many different kinds of sequences. Here the ratios of terms are constant:

  30/10 = 90/30 = 3

so the pattern could be that of a geometric sequence. In that sequence, each term is 3 times the previous one.

This pattern continues ...

  10, 30, 90, 270, 810, 2430, ...

___

Another way to look at sequences of numbers is to consider their differences. Here the differences are not constant, and there aren't enough terms to tell how the differences change.

  30 -10 = 20

  90 -30 = 60

The second of these differences can be viewed several ways. One is to say that it is 40 more than the first of the differences. If each successive difference is 40 more than the last, then the pattern is described by a quadratic function:

  $a_n=10+20(n-1)^2$

This pattern continues ...

  10, 30, 90, 190, 330, 510, ...