explicit formula for geometric sequence 80, 40, 20, 10,...

Question

So I'm supposed to write the explicit formula for the geometric sequence of 80, 40, 20, 10,... I got a sub n = 80(1/2) to the power of x? That's how my teacher wrote it, but i thought that you were supposed to do n-1 instead of x.. I'm also supposed to find the 7th term. When I did it my way i got a sub 7 = 1 1/4. But my teacher got 0.625. I'm just confused about why she did x instead of n-1.. Did I do it wrong or did she??

Answer 1

The explicit formula for a geometric sequence is usually written as:

    a_n = ar^{(n – 1)}        where   a=a₁   and  r=common ratio

 

a=80

r=(1/2)

 

   a_n = 80(1/2)⁽ⁿ⁼¹⁾

 

80, 40, 20, 10, 5, 2 1/2, 1 1/4, 5/8, 5/16, ...

 

note:  0.625 = 5/8

 

For some applications, the first element is A₀, so you may encounter that preference.