give the general term of the sequence 1,2,3,5,10,15,25,...
Type "integer sequences" in google:
Fibonacci numbers written in base 8:
1, 2, 3, 5, 10, 15, 25, 42, 67, 131, 220, 351, 571, 1142, 1733, 3075, 5030, 10125, 15155, 25302, 42457, 67761, 132440, 222421, 355061, 577502, 1154563, 1754265, 3131050, 5105335, 10236405, 15343742
When expressed in base 4, and then interpreted in base 9, is a multiple of the original number:
1, 2, 3, 5, 10, 15, 25, 75, 100, 125, 355, 435, 500, 1775, 2415, 3675, 5825, 9660, 14700, 17074, 20786, 22382, 23300, 27300, 79716, 83144, 87087, 97860, 103930, 125460, 172105, 331275, 332576, 348348, 415720, 1325100, 1330304, 1531980
The following number seems to be determined by the addition of the two previous numbers. I don't know about the connection with Fibonacci numbers.
I'm not sure about how to indicate it in general terms, but it might be something like the following:
Value (n - 2) + Value (n -1) = Value n
That isn't it, but it might help you think of the right notation. I hope it helps a little more. Thanks for asking.
Based on the given sequence 1, 2, 3, 5, 10, 15, 25,..., it seems that the numbers are increasing but not following a specific pattern like the Fibonacci numbers or any well-known integer sequence. However, there might be a relationship between the numbers that is not immediately apparent.
To find the general term of the sequence, you can try different approaches such as looking for a pattern in the differences between consecutive terms or in the ratios between consecutive terms. You can also try applying different mathematical operations, such as addition, subtraction, multiplication, or exponentiation, to see if you can identify a consistent relationship.
If you have additional information or context about how the sequence is generated or its purpose, that might also provide helpful insights into finding the general term.
Overall, without more specific information or patterns, it is difficult to determine the exact general term of the sequence. However, you can continue exploring different possibilities and mathematical operations to find a potential rule or explanation behind the sequence.