Question

I need help with arithmetic sequence

Answer 1

uh ok?

Answer 2

What is the common difference of a 57–term arithmetic sequence where the first term is –25 and the sum is 17,727? I want to learn how to solve that.

Answer 3

do you know the formula for the sum of an arithmetic sequence?

Answer 4

Yes. But, I don't know what to put where to find the common difference in the equation.

Answer 5

can you please show me the formula you are trying to use so that I can then guide you on how to use it?

Answer 6

\[s _{n} = n(a _{1}+a _{n})\div2\]

Answer 7

there is another form of the formula which involves the common difference (d) - do you know that formula?

Answer 8

\[a _{n}=a _{1}+(n-1)d\]

Answer 9

if you put these two together you will get:\[S_n=\frac{n}{2}(2a_1+(n-1)d)\]

Answer 10

can you solve it now?

Answer 11

I don't know what parts go where...

Answer 12

\(S_n\) represents the sum to n terms
\(n\) represents the number of terms
\(a_1\) represents the first term
\(d\) represents the common difference

Answer 13

it does

Answer 14

I got it I think.

Answer 15

n=57

Answer 16

\[17,727 = 57\div2(2\times-25+(57-1)d)\]

Answer 17

yes - thats right

Answer 18

\[28.5(8d) = 17,727 ?\]

Answer 19

if you are good at algebra then it might be easier to first rearrange the equation

Answer 20

did i do it right though?

Answer 21

no - it doesn't look right to me

Answer 22

try starting with:\[\frac{2S_n}{n}-2a_1=(n-1)d\]

Answer 23

then plug in the numbers

Answer 24

can you see how I got that re-arrangement or do you want me to explain it?

Answer 25

is d 12?

Answer 26

perfect! - well done!

Answer 27

Thank you :) Do you think you can help me with a few more on my assignment?

Answer 28

yw :)

please post each question separately on the left and there'll be plenty of people willing to help you in case I am busy.

Answer 29

Okay :)