Question

The sequence –12, –6, 0, 6, … , 48 has 11 terms. Evaluate the related series.

Answer 1

\[\Large a_n = a_1 +(n-1)d \]
Arithmetic

\[\Large a_1=a_1=-12 \]

Answer 2

Do you know how to define this sequence now? from there you can continue with summation notation.

Answer 3

um, im confused, i tried it

Answer 4

\[\Large a_n=a_1+(n-1)d \]
Here again, just the definition. I like to work with it, some don't. If it confuses you, you can skip that step. But basically, the sequence given above is arithmetic, this means that you add a constant \(d\) to every successful previous term.

You can derive with the formula above the value of \(d\) or by inspection of your sequence, you will see that it is 6, right?

Answer 5

\[\Large a_n=-12+(n-1)\cdot6 \]
You can check with your sequence from above that this formula works, by plugging in various numbers for \(n\)
n=1
n=2
n=3
.
.
.
n=11

Answer 6

cleaning this formula up a bit, it will look like this:
\[\Large a_n=-18+6n \]
just by algebraic notation, now do you know how to use Sums?

Answer 7

yeah, so its be 192

Answer 8

\[\Large \sum_{n=1}^{11}-18+6n=-18n+6 \left( \frac{n(n+1)}{2}\right) \]

Where n=11

Answer 9

I get 198

Answer 10

oh, i see okay