Question

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

Answer 1

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

Answer 2

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