Question

A sequence is defined recursively by

Answer 1

9514 1404 393

Answer:

  an = 4×34^(n-1)

Step-by-step explanation:

If your recursive definition is ...

  $\begin{cases}a_1=4\\a_{n}=34a_{n-1}\end{cases}$

this defines a geometric sequence with a first term a1 = 4 and a common ratio of r = 34. The general form of the explicit function is ...

  $a_n=a_1\times r^{n-1}$

For the values shown here, the explicit definition of the sequence is ...

  $\boxed{a_n=4\times 34^{n-1}}$