2010 Exam 1 Number Patterns Q4, What..?

[Deank]

Correct me if i'm wrong, but for the sum of a geometric sequence we use S(n)= (a(1-r^n))/(1-r) for |r|<1 and S(n) = (a(r^n-1))/(r-1) for |r| > 1, now in this question, the sequence clearly shows a ratio of -2, -8/4 = -2, 16/-8 = -2...etc, so for the sum of the first 10 terms, we use S10 = (4(-2^10-1))/(-2-1) which equals 1366.667, which is D.

Apparently the answer is B, and due to VCAA being oh so fantastic which their assessors reports, it says nothing about the question, thankfully Itute.com do their own worked solutions, although they do the formula for which |r| < 1, can someone explain why this is the case, perhaps I don't understand magnitude? which is that any negative value is accepted as positive, therefore |-2| = +2 and the r > 1 formula should be used, Thanks.

[DannyN]

Hello Deank, a lot of students actually made the same mistake you did.
see how you did S10 = (4(-2^10-1))/(-2-1)
which is wrong because you've forgotten to put brackets around (-2), a common mistake made by many

so your working should look like S10 = (4([(-2)^10-1]/(-2-1) =>-1364

[Deank]

Ahh kk, thank you for that, I'll be sure to watch my parenthesis during the exam.