Question

Hello everyone! I've got a question special for You.
continue the sequence: 1, 2, 3, 5, 7, 13, 21, ??

Answer 1

21,41,75

Answer 2

are the next 2 correct??

Answer 3

does 7 has to be 8, or am i wrong

Answer 4

actually 7!.
Why 41 ??

Answer 5

looking at the sequence write down the difference btwn 2 times the numberand the number succeeding it. the nos at each step .
for example
in 1,2
2 times 1=2
and hence the difference=0 if u keep doing so u get a sequence
like 0,1,1,3,1,5 so i jst guessed the next number
not sure though! are they correct

Answer 6

near true.... i think ) (but i don't know the true)

Answer 7

All numbers in the sequence are Fibonnacci numbers except the 7, so Fibonacci sequence is ruled out.

Answer 8

All numbers in the sequence are preme except 21, so no go on prime number sequence.

Answer 9

The problem with questions of this type is that the next number could be any number at all. Let's say we had \[a _{0}, a _{1},...,a _{n}\]given and I claim that the next number in the sequence is b. One way (there are infinitely many) is to create a polynomial P(x) such that \[ P(r)= a _{r}\] for r from 0 to n, and
\[P _{n+1}=b.\]
One way to find that polynomial uses techniques from the calculus of finite differences. If there are 7 terms in the given sequence, then the lowest possible degree of P(x) would be 6, so the work would be labor intensive.