#### Question

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

Question

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

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.