Question

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

Answer 1

is it -790? if not what is it?

Answer 2

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

Answer 3

my answer choices are


-813
-790
-765
-714

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

is that the formula up above?

Answer 8

no

Answer 9

No I'm wrong
I'm thinking out loud

Answer 10

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.

Answer 11

and \(S_n\) represents the sum

Answer 12

oh okay

Answer 13

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

Answer 14

... which simplifies to @asnaseer 's formula

Answer 15

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

Answer 16

now i got -714.....?

Answer 17

correct! :)

Answer 18

alright thank you!

Answer 19

yw :)