Answer:
- 2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784
- 2,490,930
- neither
- 121,800
Explanation:
1. Recursively-defined sequence
You want the first 9 terms of the recursive sequence defined by ...
The attached spreadsheet uses the given formula for the next term. It shows the terms to be ...
2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784
2. Sequence sum
The attached spreadsheet sum function has been used to find the sum of the first 8 terms. That sum is ...
2490930
3. Sequence type
The sequence of problem 1 has neither a common difference nor a common ratio between successive terms. It is neither arithmetic nor geometric.
4. Sum of arithmetic sequence
The sum of the first n terms of an arithmetic sequence with first term a1 and common difference d is given by ...
Sn = (2a1 +d(n -1))(n/2)
You have a sequence with a1 = 12 and d = (18-12) = 6. You want the sum of the first 200 terms.
S200 = (2·12 +6(200 -1))(200/2) = 121,800
The sum is 121,800.
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Additional comment
A spreadsheet is a nice tool for finding terms of a recursively-defined sequence. The formula can include as many terms as necessary, and it can be replicated thousands of times, if necessary. The limitation is that arithmetic is generally limited to 16 significant figures, or so.