Question

find the sum of the series 13 + 24 + 35 + ... + 156

Answer 1

First, we need to determine how each element of the series changes compared to the previous one. If there is a constant change between elements, then our job is pretty easy

Answer 2

Let's represent our series in variables

Answer 3

yeh its 11

Answer 4

i really dont understand how to use the finite arithmetic formula

Answer 5

Nice, so you know that 11 is being added each time, so you can determine the number of elements in the series by \[(156-13)/(d)\]

Answer 6

where d is constant difference, which you found to be 11

Answer 7

Are you saying you want represent this in sigma notation?

Answer 8

so what do i need to use the Sn = n/2 (A1 + An) for?

Answer 9

So you understand what the formula means?

Answer 10

n= the nth term and A1= 1st term
but whats the S?

Answer 11

The sum of the first n elements of the series is equal to the number of the elements divided by 2 * (the first element + the nth element you are considering)

Answer 12

S is for "sum"

Answer 13

So you need to find "n," what element number 156 is in the series

Answer 14

and 156 = A13?

Answer 15

It's actually the 13th element after the 1st one, so it's element 14, A14

Answer 16

oh

Answer 17

Yeah, basically, with (156-13)/d you are figuring out how many times you need to add 11 to 13 in order to get 156, you have to add it 13 times, so there are 13 elements after 13...

Answer 18

aww dang i thought there was a formula to try and figure that out:/

Answer 19

well, looks like it would \[(An - A1)/d+1\]

Answer 20

so whats An?

Answer 21

that is the \[n^{th}\] element in the series

Answer 22

so if im trying to find the 4th term i just plug it in there?

Answer 23

It used here too: Sn = n/2 (A1 + An) ;)

Answer 24

What do you mean by trying to find the 4th term? That equation is for finding how many elements are in the series up the nth element you are considering

Answer 25

oh im dumb i was definitely looking at the wrong problem... i see why i was soo confused

Answer 26

Oh, heh, you got it then?

Answer 27

yehh thanks!!!!

Answer 28

Thanks, no problem!