Question

Find the 4th term in the sequencewith the following definition:a1 = 2an = (a_{n-1})^2

Answer 1

The first term of the sequence is a1 = 2.

Calculating the second term (using n = 2), we have:

$\begin{gathered} a_2=(a_{2-1})^2 \\ a_2=(a_1)^2 \\ a_2=2^2=4 \end{gathered}$

The third term (n=3) is:

$a_3=(a_2)^2=4^2=16$

And the 4th term (n=4) is:

$a_4=(a_3)^2=16^2=256$

So the 4th term of the sequence is 256.