Question

Identify a pattern in each list of numbers. Then use this pattern to find the next number.

5, 12, 33, 96, 285, ___

Answer 1

Answer: 852

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Step-by-step explanation:

The given sequence is 5, 12, 33, 96, 285, ...

• The jump from 5 to 12 is +7
• The jump from 12 to 33 is +21
• The jump from 33 to 96 is +63
• The jump from 96 to 285 is +189

The sequence of increases is: 7, 21, 63, 189

Then notice,

• The jump from 7 to 21 is "times 3"
• The jump from 21 to 63 is also "times 3"
• The jump from 63 to 189 is also "times 3".

Assuming this pattern keeps up, the next increment will be 189*3 = 567

We add this increment to the last term of the original sequence

285+567 = 852

The sequence is now 5, 12, 33, 96, 285, 852, ...