Find the first four (4) terms of the sequence if An = (4) an-1 and a1 = 1/2.

Seems to be

an=4 (an-1)

means the nth term is 4 times the previus term

easy, times each term by 4

so 2nd is 4*1/2 or 2

3rd term is 2 times 4 or 8

4th term is 8*4=32

first 4 terms are 1/2, 2, 8, 32

If the recursive formula is:

a (n) = 4*a (n-1)

And a1=1/2

This is a geometric sequence because each term is a constant multiple of the previous term, this constant multiple is called the common ratio. Any geometric sequence can be expressed as:

a (n) = ar^ (n-1), a (n) = nth term, a=initial term, r=common ratio, n=term number

In this case, a=1/2 and r=4 so

a (n) = (1/2) (4^ (n-1)), so the first four terms are:

4^0/2, 4^1/2, 4^2/2, 4^3/2

1/2, 4/2, 16/2 64/2

1/2, 2, 8, 32