Did I just spend 3 hours failing to work out a maths question. Cried, took a break, came back and got it straight away?

@SeductiveCactus Well first we check if it's an arithmetic or geometric series.

Checking for a geometric series:

a2/a1 = -7/3 = q
a3/a2 = -11/7 /= q
for it to be geometric a2/a1 = a3/a2 but it doesn't so it must be an arithmetic series, or it's not a series at all.

Now we look for simple patterns, we can see that every other number becomes negative. This means that it's multiplied by -1 that's raised to the power of k that's odd and even every other step in the series.

If we negate this change by making all numbers even, since we know that we need to find d = difference between each step, we can now take 7 - 3 = 15 - 11 = 19 - 15 which is indeed = 4

We now know that d = 4

we know that there's 7 numbers (steps) in the function, so we start with:
.7
.E(4k) = 4, 8, 12... etc
k=1

this doesnt look quite right, all the numbers should be odd, and if we compare the series each step in our series should be exactly 1 less. We try again.

.7
.E(4k - 1) = 3, 7, 11..
k=1

now we're getting close. We know that we need to make the first number negative, the second number positive, so on so forth. That's why we set -1^k

.7
.E(4k - 1)(-1)^k = -3, 7, -11...
k=1

and that's the workflow

@MartinTheFirst Ohhhhhhhh. Thank you so much. Explaining it really helped my understanding. I definitely need to study up more but now I think I know where to start when doing these types of questions. Just need some practice haha. I now know where to go to ask about this subject haha 😂

@SeductiveCactus MagnifiqueGirl can have the best answer on my behalf

@JoyfulSilence oh really? That's pretty cool. I enjoy maths, but I often find I always seem to make small mistakes and it messes with my final answer. And it gets so frustrating when I fell like I'm stuck on a real simple question. 🤯

@SeductiveCactus Yes. In college I graded math homework and so many errors were little. Proofreading helps. And breaking things out into little steps.

@Mordi oh it wasn't? Well then

Well then exactly.

@SW-User haha I wish I could have up. But it was apart of an assignment and cause of corona virus made out classes online, assignments were made to be worth more of our final grade.