I need help with pattern

Question

-2,20,-200,2000,... Yeah i need help with it thank you and have a good day and night

Answer 1

the terms are 10 times bigger (2,20,200 etc) but also changing sign (-2, +20, -200 etc). This is a geometric sequence with a constant of -10.

hence a_n = -10(a_n-1)

this lets you figure out the next or previous number, given any number in the pattern. However, I'm sure you can see that it's not specific to our pattern yet (it could apply to -100, 1000, -10000 for example, which is a different series).

To be specific to -2, 20, -200, 2000... I need to start with -2 as the first term (n=1), instead:

hence a_n = -2.(-10)^(n-1)

which probably looks a bit complicated, so maybe easier if I show the first few terms to see how this works:

a₁ = -2.(-10)^(1-1) = -2.(-10)⁽⁰⁾ = -2 x 1 = -2

a₂ = -2.(-10)^(2-1) = -2.(-10)⁽¹⁾ = -2 x -10 = 20

a₃ = -2.(-10)^(3-1) = -2.(-10)⁽²⁾ = -2 x 100 = -200

a₄ = -2.(-10)^(4-1) = -2.(-10)⁽³⁾ = -2 x -1000 = 2000

Answer 2

It alternates negative then positive

ignoring the sign, the terms have a common ration of 10

An+1 = 10An, the absolute value of each term is 10 times the prior term

2

20

200

2000

then just alternate the sign

An+1 = -10An.

Each term is -10 times the prior term

with A1 = -2

A2 = -10A1 = -10(-2) = 20

A3 = -10A2 = -10(20) = -200

A4 = -10A3 = -10(-200) = 2000

It's a geometric sequence with a common ratio of -10

-2(10^0), -2(-10^1), -2(-10)^2, -2(-10)^3, -2(-10)^4, ... -2(-10)^n

the power of -10 increases by one each succeeding term in the sequence