SOLUTION: hey, can you point me in the right direction for writing an equation for the geometric sequence -10, 5, -5/2...... i know a_1 = -10 , and r= -1/2

Algebra ->  Sequences-and-series -> SOLUTION: hey, can you point me in the right direction for writing an equation for the geometric sequence -10, 5, -5/2...... i know a_1 = -10 , and r= -1/2       Log On


   

Question 307271: hey, can you point me in the right direction for writing an equation for the geometric sequence -10, 5, -5/2......
i know a_1 = -10 , and r= -1/2
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a reference that might help you.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm

The nth term in a geometric sequence is given by the equation:

an = a1*r(n-1)

If a1 is equal to -10, and r is equal to -.5, then you have your equation of:

an = -10 * (-.5)(n-1)

For example:

If n = 5, then an = (-10) * (-.5)(n-1) becomes:

a5 = -10 * (-.5)(5-1) which becomes:

a5 = -10 * (-.5)(4)

That would be equal to -.625

You start with -10
Multiply it by -.5 to get 5 (first time)
Multiply that by -.5 to get -2.5 (second time)
Multiply that by -.5 to get 1.25 (third time)
Multiply that by -.5 to get -.625 (fourth time)

You multiplied by -.5 four times which is equivalent to multiplying by -.54