Question

what is the sum of the arithmetic sequence 135,123,111... if there are 34 terms?

Answer 1

what is the difference between the 2nd term and the 1st term?

Answer 2

123 - 135 = ?

Answer 3

12.

Answer 4

Dude ,Try to solve your own exam by your own ,believe me.....u gonna solve it faster.

Answer 5

lets go with -12 :) this is our common difference (d).

Answer 6

ok.

Answer 7

we can use the formula:

an = a1 + d(n-1)

to find the last term that we will need

Answer 8

when n=34 we get:

a34 = 135 -12(33)

whats tat get us?

Answer 9

a34= 135- 396?

Answer 10

keep going, so far so good

Answer 11

i dont kow how to keep going.

Answer 12

135 - 396 = ??

Answer 13

-261

Answer 14

good; this is our last term in the sequece that we need

Answer 15

now we need to use another nifty little formula:

\[Sn=\frac{n}{2}(a1+an)\]

Answer 16

\[S_{34}=\frac{34}{2}(135-261)\]

Answer 17

@amistre64 where can I find proof for that formula?

Answer 18

okay... now?

Answer 19

now thats the answer

Answer 20

no its not. its not an option.

Answer 21

the proof is pretty simple xcrypt

suppose we have an arith seq: a1 to an

Answer 22

try doing the math to finish it out; im not your nanny

Answer 23

i know its a negative.

Answer 24

so is it like, -2,108?

Answer 25

\[A = a_1+a_2+a_3+...+a_n\]

to sum this up we can add it together twice, but in a useful way, reverse the second set

\[A = a_1+a_2+a_3+...+a_n\]\[A = a_n+a_{n-1}+a_{n-2}+...+a_1\]

that gets us

2a = (a1+an) + (a1+an) + ... + (a1+an) ; n times

Answer 26

was my answer correct?

Answer 27

@Ethan96 use a calculator? Or just type in the equation in google

Answer 28

17*(-126) i believe

Answer 29

-2,142

Answer 30

divide both sides by 2 to get:

\[A=\frac{n}{2}(a_1+a_n)\]

Answer 31

okay,so -2,142 is correct? :D

Answer 32

that looks better yes

Answer 33

THANKS

Answer 34

theres other proof, but that ones the one i like

Answer 35

hmm great, thanks! What's this topic called in math? Never seen it before

Answer 36

series and sequences is usually when it comes about, but that little tidbit also comes up in discrete math

Answer 37

okay thanks ^^