3 4 9 8 9 8 13 14 13 ?
So what is the next number?
Hint
the actual difference between numbers is just 1 and the sequence actually starts with 1.
Hint
Spelling is the key!
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Sign up to join this community3 4 9 8 9 8 13 14 13 ?
So what is the next number?
Hint
the actual difference between numbers is just 1 and the sequence actually starts with 1.
Hint
Spelling is the key!
Going for the obvious here.... (because someone has to..)
14.
The whole thing is very arbitrary. Goes from 3 -> 4 then jumps up 6 and sequences 1 down 9 -> 8 -> 9 -> 8 and then jumps up 6 again (from 8 to 14: just wrote this for the sake of some sort of pattern) and sequences up 13->14->13->14.
Very disappointed if this is the answer :-{
I think the answer is
12
The formula for generating the $n$th term in the sequence is
$n$ + 2*(number of letters in English spelling of $n$) - 4
For example the first term in the sequence is
1 + 2*3 - 4 = 3
The 9th term is
9 + 2*4 - 4 = 13
And so the 10th term is
10 + 2*3 - 4 = 12
In relation to the hints
The underlying sequence is the positive integers beginning at 1 and generation of the sequence depends on the spelling of the numbers.
Consider the following polynomial:
$$P(x) = 898-k-\frac{507793}{210}\cdot x-\frac{5}{192}\cdot kx^6+\frac{3013}{17280}\cdot kx^5-\frac{95}{128}\cdot kx^4+\frac{4523}{2268}\cdot kx^3-\frac{6515}{2016}\cdot kx^2+\frac{7129}{2520}\cdot kx+\frac{1092977}{420}\cdot x^2+\frac{1}{362880}\cdot kx^9-\frac{1}{8064}\cdot kx^8+\frac{29}{12096}\cdot kx^7-\frac{5}{4032}\cdot x^9-\frac{7552313}{5040}\cdot x^3+\frac{41377}{80}\cdot x^4-\frac{107677}{960}\cdot x^5+\frac{77}{5}\cdot x^6-\frac{4363}{3360}\cdot x^7+\frac{103}{1680}\cdot x^8$$
It is a straightforward calculation to check that:
So it might be that there are multiple solutions?
It's not 100% convincing, but worth a try:
3 4 9 8 9 8 13 14 13 ?
Numbers 3, 6, 9: 9, 8, 13 (no idea. Typo? :)
Numbers 2, 5, 8: 4, 9, 14 (+5)
Numbers 1, 4, 7: 3, 8, 13 (+5)
Number 10: 13 + 5 = 18
I thought the question would be solved after giving Hint 1 and Hint 2 but I could not get the right one.
Methodology
Since the sequence starts with 1 and increases by 1 (Hint 1) and spelling was important (Hint 2), You needed to check the spelling of 1, which is one. There are two vowels and one consonant and the generalization is found from here;
Equation
Number + (# of Vowels)x(# of Consonants)
The Answer
For 10, ten has two consonants and one vowel so 10+2x1=12.