Consider the following geometric sequence -5,10,-20, if the reclusive formula for the sequence above is expressed in the form a^n = b*a^n-1 , determine the value of b

Hello from MrBillDoesMath!

  b = -2

Discussion:

Let's analyze this sequence.  

The first number = -5                               a(0)

The second number = 10 = -5 (-2)          a(1) = a(0) *-2

the third number  = -20 = 10 * (-2)          a(2) = a(1) * -2

The fourth number = -20 * (-2)                a(3) - a(2) * -2

In other words, the recursive (not reclusive) formula is

a(0) = -5         (this need to be stated! Not stated in the problem)

a(n) = a(n-1) * (-2)

This implies that "b" = -2.

Regards, MrB

d

step-by-step explanation: