Write the sum using summation notation, assuming the suggested pattern continues. 2, -10, 50, -250, +…

Is this sequence arithmetic or geometric? How do you know?

Step-by-step explanation:

An arithmetic sequence is of the form:

While a geometric sequence is of the form:

notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.

In fact, the pattern is kinda easy to see.

The first term is:

A₁ = 2

the second term is:

A₂ = -10

notice that:

A₂/A₍ = r = -10/2 = -5

The third term is:

A₃ = 50

the quotient between the third term and the second term is:

A₃/A₂ = 50/-10 = -5

Whit this we can already conclude that the n-th term of our sequence will be:

Then the summation will be something like:

We can write:

Then the summation is just:

question:

could we have options?

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb