To find the next three terms in the sequence 2, 5, 10, 17, 26, we first need to identify the pattern in the series.
Let’s look at the differences between consecutive terms:
- 5 – 2 = 3
- 10 – 5 = 5
- 17 – 10 = 7
- 26 – 17 = 9
The differences are: 3, 5, 7, 9. We can see that these differences are increasing by 2 each time.
If we continue this pattern, the next difference would be:
- 9 + 2 = 11
Now we add this difference to the last term in the original sequence:
- 26 + 11 = 37
Next, we continue finding the differences:
- 11 + 2 = 13
Now add 13 to the last number we calculated:
- 37 + 13 = 50
Continuing one more time:
- 13 + 2 = 15
Now add 15 to the previous sum:
- 50 + 15 = 65
So, the next three terms in the sequence are 37, 50, and 65.
In conclusion, the extended sequence is 2, 5, 10, 17, 26, 37, 50, 65.