Question

Use differences to find a pattern in the sequence.

2, 14, 74, 242, 600, 1252, 2324.
Assuming that the pattern continues, what should be the eighth term?

Answer 1

To find the pattern in the sequence, calculate the differences between consecutive terms and observe the relationship. Continuing the pattern, the eighth term of the sequence should be 3408.

Step-by-step explanation:

To find the pattern in the sequence, we need to look at the differences between consecutive terms. Let's calculate the differences:

14 - 2 = 12

74 - 14 = 60

242 - 74 = 168

600 - 242 = 358

1252 - 600 = 652

2324 - 1252 = 1072

The differences seem to be increasing by 12 each time. So, if we continue this pattern, the eighth difference should be 1072 + 12 = 1084. To find the eighth term, we add this difference to the last term in the sequence: 2324 + 1084 = 3408.