Question

If a_1=2a 1 ​ =2 and a_n=(a_{n-1})^2-2a n ​ =(a n−1 ​ ) 2 −2 then find the value of a_4a 4 ​ .

Answer 1

9514 1404 393

Answer:

  2

Step-by-step explanation:

We assume your recursive formula is ...

  $a_1=2\\a_n=a_{n-1}^2-2$

Using this to find a4, we get ...

  $a_2=a_1^2-2=2^2-2=2\\a_3=a_2^2-2=2^2-2=2\\a_4=a_3^2-2=2^2-2=2\\\\\boxed{a_4=2}$