Question

Given the two terms in a geometric sequence how do you find the recursive formula... a1=-4 and a4=-500?

Answer 1

Answer:

(-4)(-5)^(n-1)

Step-by-step explanation:

In a geometric sequence, we know that every term is being multiplied by a special number to get the next term. Let that special number be ' r '

As a1= -4

So the next i.e a2 must be a1 multiplied by r

therefore a2 = -4r

similarly a3 must be a2 multiplied by r

therefore a3= -4r x r = -4r^2

And so a4 must be -4r^3

But we already know that a4 = 500,

so we can say that -4r^3=500

and so r= -5 ( now we know the special number that was being multiplied with each term to get the next term)

The formula for the nth term of a geometric equation is

ar^(n-1)   (where a is the first term and r is that special number that is multiplied every time)

So nth term formula = (-4)(-5)^(n-1)