Question

Find the sum of the arithmetic sequence.

17, 19, 21, 23, ..., 35 PLEASE

Answer 1

Answer is 260 (: I can't explain, i suck at explaining dude, sorry. plus i gotta go.

Answer 2

Hope I helped you.

Answer 3

http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

Answer 4

gives the derivation

Answer 5

so we use the equation to find a sequence term as => \(\bf \Large a_n = a_1+(n+1)d\)

Answer 6

so looking at -> 17, 19, 21, 23, ..., 35 <-
we see the 1st term, \(\bf a_1 = 17\)
the common ratio is "2", 2 is being added to the previous term to get the next

we also see a 35 in the end, what term is that? dunno

but we know that \(\bf a_n = a_1+(n+1)d\)
so let's use those values and solve for "n" so we can see what that term is

\(\bf a_n = a_1+(n+1)d \implies 35 = 17+(n+1)2\\
35 = 17+ 2n+2 \implies 35 = 2n+19 \implies 16 = 2n\\
8 = n \textit{, so we now know that 35 is the } 8^{th}\ term\)

Answer 7

so you'd think, who cares?

well, now we'll use the Sum of a partial sequence equation of \(\bf \Large S_n = \cfrac{n}{2}(a_1+a_n)\)

Answer 8

so we know that our end term in the sequence is the 8th term, 35
we know our 1st term, 17

thus \(\bf S_n = \cfrac{n}{2}(a_1+a_n) \implies S_8 = \cfrac{8}{2}(17+35)\)

Answer 9

Ahhh okay! i am understanding, I had no idea how to get the n :D

Answer 10

S8 would be 208?

Answer 11

yes

Answer 12

what do we need s8 for?

Answer 13

s8 is the "sum of the arithmetic sequence"

Answer 14

it's just the notation saying, Sum of 8 terms of this sequence

Answer 15

ahhh but that isn't the whole sum right? bc that's not an answer choice

Answer 16

well, that's what I got from the Sum equation.... so what choices do you have?

Answer 17

260

179

37

160