In the sequence $$ 1,1,2,3,5,8,x,21,34,55,\dots $$, what is the estimated value for $$ x $$

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Uniteasy Admin · Accepted Answer

By observation, the sequence $$ 1,1,2,3,5,8,x,21,34,55,\dots $$
follows the attribute of a recursive sequence starting from the second term
$$ a_{n+2} = a_{n+1} +a_n $$
Therefore 
the value of $$x = 5+8 = 13$$
Checking
the values of following two terms are 21 and 34
$$34 = 21+13$$
which shows that the value of $$x = 13$$ still follows the rule of the recursive sequence.

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