Question

I need math help. If youre solving a geometric sequence, the equation needed is An=A1Rn-1. If A1= 5 and R= -2. My question was "Find the 6 numbers in this geometric sequence." The answer is : 5, -10, 20, -40, 80, -160.
I dont understand how the sequence goes from postive numbers to negative numbers? I got all the same numbers except mine were all negative.

Answer 1

Answer:

Step-by-step explanation:

an = a1 * r^(n - 1)

a1 = first term = 5

r = -2

n = nth term of the sequence

so it starts with 5

second term is :

an = a1 * r^(n - 1)......for second term

a2 = 5 * -2^(2 - 1) =

a2 = 5 * -2^1

a2 = 5 * -2

a2 = -10

an = a1 * r^(n - 1)....looking for a3

a3 = 5 * -2^(3 - 1)

a3 = 5 * -2^2

a3 = 5 * 4

a3 = 20

an = a1 * r^(n - 1)....looking for a4

a4 = 5 * -2^(4 - 1)

a4 = 5 * -2^3

a4 = 5 * -8

a4 = - 40

an = a1 * r^(n - 1)...looking for a5

a5 = 5 * -2^(5 - 1)

a5 = 5 * -2^4

a5 = 5 * 16

a5 = 80

an = a1 * r^(n-1)...looking for a6

a6 = 5 * -2^(6 - 1)

a6 = 5 * -2^5

a6 = 5 * -32

a6 = -160