To find the 8th term of the pattern, we first need to identify the pattern itself. Looking at the numbers given, we can see that each subsequent number is obtained by multiplying the previous number by 5 and then subtracting 1. So, the pattern is: 3, 35-1=14, 145-1=69, 695-1=344, 3445-1=1719. Continuing this pattern, the 8th term would be 6249.
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Well, honey, to find the 8th term of that pattern, you first need to realize it's increasing by multiplying by 6, then adding 1, then adding 80, then adding 400, and so on. So, if you keep that pattern going, the 8th term would be 12499. Don't say I never did anything for you!
Any number that you choose can be the 8th term. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the chosen eighth number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
Having said that, the simplest answer, based on a polynomial of order 4, is 46259.
It is 917969.
It is possible to find a polynomial of degree 5 such that it can be made to fit the pattern of the above five numbers and any number at all that is chosen to be the eighth. However, the simplest polynomial of degree 4 is Un = 36n4 - 336n3 + 1128n2 - 1568n + 741 for n = 1, 2, 3, ... and accordingly, the 8th term is 35,813.
90
Well, darling, the sequence you've got there is just the perfect squares of numbers. The 8th term would be the square of the 8th number, which is 64. So, the 8th term of the sequence 1, 4, 9, 16, 25 is 64. Keep those brain cells sharp, honey!
It is: 1 1 2 3 5 8 13 and 21 which is the 8th term