Please answer with explanation! Lots of points and brainliest!!

The common ratio is r = -2 because we multiply each term by -2 to get the next term. Alternatively, divide each term by its previous one to get r = -2

We want the sum of the first n = 10 terms

The formula we'll use is

S(n) = a*(1-r^n)/(1-r)

so let's plug in the given info and compute

S(n) = a*(1-r^n)/(1-r)

S(10) = 4*(1-(-2)^10)/(1-(-2))

S(10) = 4*(1-1024)/(1+2)

S(10) = 4*(-1023)/3

S(10) = -4092/3

S(10) = -1364

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If you wanted to, you can generate the first ten terms to be

4, -8, 16, -32, 64, -128, 256, -512, 1024, -2048

Then add them up

4+ (-8)+ 16+ (-32)+ 64+ (-128)+ 256+ (-512)+ 1024+(-2048) = -1364

This confirms we have the right answer.

This method is only advised for relatively small values of n

For larger values of n, use a spreadsheet program to quickly generate all the terms and quickly add them up (using the SUM function).

Because you're in an algebra class, your teacher will most likely want you to use the formula mentioned in the prior section. Also, it saves a lot of time to use the formula.