## anonymous one year ago Find S7 for the geometric series 2 + -6 + 18 + -54 +… i got 1450?

1. anonymous

Almost. What is the common ratio?

2. anonymous

3

3. anonymous

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

4. anonymous

-3

5. anonymous

That's it.

6. anonymous

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?

7. anonymous

-4374?

8. anonymous

Not quite. $-54 \times -3 \times -3 \times -3 = ?$

9. anonymous

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

10. anonymous

It sure is.

11. anonymous

Why do you think it's incorrect?

12. anonymous

the answer choices are 162 -486 1094 -4374

13. anonymous

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?

14. anonymous

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.

15. anonymous

That will give you the correct answer.

16. anonymous

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