Question

Find S7 for the geometric series 2 + -6 + 18 + -54 +…
i got 1450?

Answer 1

Almost. What is the common ratio?

Answer 2

3

Answer 3

So close. What about the change in sign every term?

Answer 4

-3

Answer 5

That's it.

Answer 6

Now, four terms are given, and you need the 7th term. So, take the 4th term (-54) and multiply by the common ratio three more times. What do you get?

Answer 7

-4374?

Answer 8

Not quite. \[-54 \times -3 \times -3 \times -3 = ?\]

Answer 9

I got 1458... that's not right though.

Answer 10

It sure is.

Answer 11

Why do you think it's incorrect?

Answer 12

the answer choices are
162
-486
1094
-4374

Answer 13

OK. Perhaps it's a notation issue. Perhaps, when the questions asks for S7, what they want is the SUM of the first 7 terms. Could that be it?

Answer 14

If so, to calculate the sum of the first n terms of a geometric series, use\[\sum_{i=1}^{n} a_i = a \left( \frac{ 1-r^n }{ 1-r } \right)\]where a is the 1st term, r is the common ratio, and n is the number of terms to be summed.

Answer 15

That will give you the correct answer.

Answer 16

\[S_7 = 2\left( \frac{ 1-\left( -3 \right) ^7}{ 1-\left( -3 \right) } \right) = ?\]