OpenStudy (anonymous):

What is the sum of a 17-term arithmetic sequence where the first term is 6 and the last term is -90?

OpenStudy (anonymous):

is it -790? if not what is it?

OpenStudy (anonymous):

Hmm... x(0) = 6, x(n+1) = x(n)+d, x(16)=-90...

OpenStudy (anonymous):

my answer choices are -813 -790 -765 -714

OpenStudy (anonymous):

\[d = \frac{x(16)-x(0)}{16}\]

OpenStudy (anonymous):

\[x(0) + \sum_{k=0}^{16}(d)\]

OpenStudy (asnaseer):

@sammysweets do you know the formula for the sum of an arithmetic sequence in terms of its first and last terms?

OpenStudy (anonymous):

is that the formula up above?

OpenStudy (asnaseer):

no

OpenStudy (anonymous):

No I'm wrong I'm thinking out loud

OpenStudy (asnaseer):

you can find the various formulas for an arithmetic sequence here: http://en.wikipedia.org/wiki/Arithmetic_progression in this case, the formula you need to use is:\[S_n=\frac{n}{2}(a_1+a_n)\]where n is the number of terms, \(a_1\) is the first term, and \(a_n\) is the last term.

OpenStudy (asnaseer):

and \(S_n\) represents the sum

OpenStudy (anonymous):

oh okay

OpenStudy (anonymous):

\[x(0) + \sum_{k=1}^{16}(k*d)\]

OpenStudy (anonymous):

... which simplifies to @asnaseer 's formula

OpenStudy (asnaseer):

yes - @fredrickV was trying to derive the formula from first principals.

OpenStudy (anonymous):

now i got -714.....?

OpenStudy (asnaseer):

correct! :)

OpenStudy (anonymous):

alright thank you!

OpenStudy (asnaseer):

yw :)