The nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
What are sequences?
Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.
We can find the nth term of the given sequences as follows:
It is given that the nth term of the sequence 1, 4, 9, 16... is n squared.
- We can find the nth term of the sequences 2, 5, 10, 17... as shown below:
2, 5, 10, 17...
1² + 1, 2² + 1, 3² + 1, 4² + 1...
This is of the form n² + 1. The nth term can be found using the formula n² + 1.
- We can find the nth term of the sequences 2, 8, 18, 32... as shown below:
2, 8, 18, 32...
2×1², 2×2², 2×3², 2×4²...
This is of the form 2n². The nth term can be found using the formula 2n².
Therefore, we have found that the nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
Learn more about sequences here: https://brainly.com/question/7882626
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