[Anon26]

An easy one:

1, 2, 10, 140, 5740, ?

[Guest]

700280, will post reason if correct

[Anon26]

you got that right

[Guest]

Here's how each term in the sequence is determined: the first term is 1, and we'll call the first "factor" 2. The next term in the sequence is always the product of the term and its factor, and the next factor is defined to be 3 times the current factor, less 1. So the factors are 2,5,14,41,122, etc

[Anon26]

Well Matho, I think you got it wrong (or I failed to understand your reasoning coz ans is pretty simple), there is rather a simple explanation which I wont disclose now because that will spoil the fun for those who want to solve

James22 answer is correct

[Guest]

Matho’s reasoning to derive the factor to multiply the previous number by seems quite reasonable:

The beginning of the sequence is 1, the explanation just gives you the factor used to multiply the previous number by.

(1*3)-1=2, thus 2*1=2

(2*3)-1=5, thus 5*2=10

(5*3)-1=14, thus 14*10=140

(14*3)-1=41, thus 41*140=5740

(41*3)-1=122, thus 5740*122=700280

[Anon26]

Mine was simpler:

Divide each number by number before it you get a new series:

1,2,10,140,5740 >>> 2, 5 , 14 , 41

Now subtract each number by number before it you get a new series:

2, 5 , 14 , 41 >>> 3, 9, 27

The new series above is pretty clear, the next would be 81. Now we take it back above to the first series and it is 700280

[Guest]

Depends on what you call simpler, there’s always more than 1 way to skin a cat some people may see the series:

1,4,9,16,25,36,49 and see it as the squares of consecutive number, while others may see it as a series that starts with the odd number 1, and then adds the next odd number to get the series, in other words, 1, then 1+3 (4), then 4+5 (9), the 9+7 (16), then 16+9 (25), 25+11 (36), 26+13 (49),etc….

For the series given in the question, I consider using a formula of((3*N)-1)*N to arrive at the next number quite simple

[Guest]

The formula I sent was incorrect((3*previous factor)-1)*N

[Anon26]

I saw that but

GooD WorK!