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

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

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) (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:

a_n = a₁*r^(n-1)

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

a_n = -10 * (-.5)^(n-1)

For example:

If n = 5, then a_n = (-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

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