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Use differences to find a pattern in the sequence.

7​, 10​, 17​, 33​, 63​, 112​, 185



Assuming that the pattern​ continues, the eighth term should be

Verified Answer :

Answer:

519

Step-by-step explanation:

The difference between 10 and 7 is 3.

The difference between 17 and 10 is 7.

The difference between 33 and 17 is 16.

The difference between 63 and 33 is 30.

The difference between 112 and 63 is 49.

The difference between 185 and 112 is 73.

Observing these differences, we notice that they follow a pattern:

3, 7, 16, 30, 49, 73

Looking closely, it seems like each difference is increasing by consecutive odd numbers: 1^2, 3^2, 5^2, 7^2, 9^2, 11^2.

So, if we continue this pattern:

The difference between 185 and the next term would be 185 + 13^2 = 334.

Adding this difference to 185, we get the eighth term: 185 + 334 = 519.

Therefore, the eighth term in the sequence should be 519.

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