How to Solve Arithmetic Sequence Problems

[Purpleshinyrock]

Summary:: Sequences, Progressions

Hello. I have been Given the following exercise, Let (a1, a2, ... an, ..., a2n) be an arithmetic progression such that the sum of the last n terms is equal to three times the sum of the first n terms. Determine the sum of the first 10 terms as a function of the ratio d.

Solution is S10=50d

I know that an=a1+nd-d, and an+1=a1+nd
a2n=a1+(2n-1)d=a1+2nd-d

sn=(a1+an)(n/2)=(2a1+nd-d)(n/2)
Sn=(an+1+a2n)(n/2)=(2a1+3nd-r)(n/2)
But When I try to do Sn=3sn(the sum of the last n terms is equal to three times the sum of the first n terms) I am not getting the desired result.
Could someone please help me?

[Moderator's note: Moved from a technical forum and thus no template.]

 

[mfb]

A ratio is the result of a division, e.g. a/b. I assume you mean "difference" d.

Sn=(an+1+a2n)(n/2)=(2a1+3nd-r)(n/2)

What is r?

But When I try to do Sn=3sn(the sum of the last n terms is equal to three times the sum of the first n terms) I am not getting the desired result.

The approach is good so far (after fixing the r). Please show your following work, otherwise it's impossible to tell what went wrong.