Number Sequence Question from Advanced Quant Book

[hkparikh09]

What should the next number in the sequence be?

1, 2, 9, 64, X

I understand the pattern identified by MG:

1^0, 2^1, 3^2, 4^3

The pattern in the bases is 1, 2, 3, and 4
The pattern in the exponents is 0,1,2,and 3

So the next number in the sequence should be 5^4=625

However, I found a different pattern, and I get a different answer. The pattern I identified was in the differences between each number.

Differences:
2-1 = 1

9-2 = 7

64 - 9 = 55

So the pattern in the differences is:
1^2 +6 = 7

7^2 +6 = 55

So I figured that the next number in the sequence should be:

64 + (55^2) + 6 = 3,095

What am I misunderstanding about the pattern I identified? My answer and MG's answer are completely different.

[jnelson0612]

What should the next number in the sequence be?

1, 2, 9, 64, X

I understand the pattern identified by MG:

1^0, 2^1, 3^2, 4^3

The pattern in the bases is 1, 2, 3, and 4
The pattern in the exponents is 0,1,2,and 3

So the next number in the sequence should be 5^4=625

However, I found a different pattern, and I get a different answer. The pattern I identified was in the differences between each number.

Differences:
2-1 = 1

9-2 = 7

64 - 9 = 55

So the pattern in the differences is:
1^2 +6 = 7

7^2 +6 = 55

So I figured that the next number in the sequence should be:

64 + (55^2) + 6 = 3,095

What am I misunderstanding about the pattern I identified? My answer and MG's answer are completely different.

Hi there,
Your pattern would explain how I get from 2 to 9 and from 9 to 64. But how would your pattern account for how I get from 1 to 2? The pattern has to help us get from each value in the sequence to the next. I look forward to hearing from you!