Question

[PRECAL HELP~*] Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 4 + 1 + 6 + ... + 66

Answer 1

Is this an arithmetic sequence or a geometric sequence?

How do you know?

If you start with -9 and find that your next term in the sequence is -4, what had you done to that first term (-9)?

Answer 2

added positive 5

Answer 3

that's right! So, have we an arithmetic or a geom. sequence here?

Answer 4

arithmetic

Answer 5

Very good!

Now, please look up "sum of an arithmetic sequence" anywhere you think appropriate: in your textbook, in your online learning materials, through an Internet search, whatever. by doing this you'll find a formula for the sum of an arithmetic sequence of n elements.

Answer 6

is it this one?

Answer 7

or this one

Answer 8

Yes and no. If you were to find all of the terms of the sequence and then add them together, you'd get the sum of the sequence.

But there's another formula that requires you to add only the first and last terms of the sequence and to multiply the result by n/2, where n is the number of terms you're adding together.

What is that formula?

Hint: see:

http://www.purplemath.com/modules/series4.htm

Answer 9

so -9 + 66 (5/2) ?

Answer 10

First, are you sure that there are only 5 terms in this sequence?
Secondly, it's very important that you enclose that -9+66 inside parentheses. Otherwise others would think you're multiplying only 66 by (5/2).

Answer 11

ohh I forgot about the (...)

Answer 12

I see you've counted the number of visible terms and decided that n = 5 based upon that. But that's not right.

Hint: There's another very useful formula that applies here: l=a + (n-1)d. Have you seen this before?

Answer 13

no

Answer 14

a= first term
l= last term
n= number of terms (which is what you want)
d= the number you keep on adding to each most recent term to get the next term.

Answer 15

At this point, you have a choice:

1) write out all the terms, from -9 through 66, or
2) use this formula I've given you, to find a) n-1 and b) n.

Answer 16

66= -9 + (n-1)

Answer 17

75=n-1

Answer 18

Hint: don't forget that ' d '. ' d ' = 5,

Answer 19

75= (n-1) 5

15=(n-1)

Answer 20

Nice work! So, n = ??

Answer 21

16?

Answer 22

Great! Your arith. sequence has 16 terms.

Now go back to the formula for calculating the sum of the first n terms:

(a + l)(n/2).

Answer 23

a=-9
d=?
l=?
n=?

Answer 24

(-9 +66) (16/2) = 456?

Answer 25

Surely looks good! Congrats. Any questions?

Answer 26

Thank you :D though the answer options are a little different:

Answer 27

In those answer options, you see the Greek letter sigma in each: \[\sum_{}^{}\] what does that represent in this arithmetic sequence problem?

Answer 28

the sum

Answer 29

Right. That "sigma" represents "summation."

Now look at the lower limit and the upper limit on each sigma. Supposing n (a counter, like counting on your fingers) starts at 0 and ends at 15. How many terms would you be adding up?

Answer 30

16

Answer 31

Right. See what I'm driving at? Does this give you enuf info to choose the correct answer, or would you like to discuss further how to identify the correct answer?

Answer 32

is it the second one?

Answer 33

Yes.

You could check your answer as follows:

-9+0(5) =-9
-9+1(5) =-4
-9+2(5) = 1
and so on....
and you'd find that the sum of these 16 terms is 456.

Again, nice work!

Answer 34

I need to get off the 'Net now, but look forward to working iwth you again in the future!

Answer 35

Thanks you very much for your wonderful help <3