A sequenceis defined recursively by the equation for where . Use your calculator to guess the limit of the sequence.
B)13
E)12

Question

A sequenceis  defined recursively by the equation  for  where  . Use your calculator to guess the limit of the sequence.
B)13 
E)12

Quizplus · Accepted Answer

Since the given equation is defined recursively, calculating the first few terms of the sequence gives:
a1 = 11eaa3e5_5513_a3ed_9f8f_17dc25d8f0f4_TB5971_11
a2 = 11eaa3e5_5513_a3ee_9f8f_69f040a4a4f5_TB5971_11
a3 = 11eaa3e5_5513_a3ef_9f8f_954c4465e508_TB5971_11
a4 = 11eaa3e5_5513_a3f0_9f8f_93086f5ac02e_TB5971_11
and so on.

It is not possible to find a closed-form expression for the sequence, so we cannot use algebraic methods to find the limit. However, we can observe that the first few terms of the sequence are all around 12, so it is reasonable to guess that the limit of the sequence is also 12. Therefore, the best choice is E.

A Sequenceis Defined Recursively by the Equation for