Sequences: sum of 1st 2 terms is 18, sum of 1st 4 is 52

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
pederjohn
Posts: 1
Joined: Thu Jun 18, 2009 8:20 pm
Contact:

Sequences: sum of 1st 2 terms is 18, sum of 1st 4 is 52

Postby pederjohn » Thu Jun 18, 2009 8:22 pm

Well i am now totally lost...

I want so to solve this maths problem on my own but i have no idea how to solve it... I can solve it the long way but how can i do it quicker?

Code: Select all

The sum of the first two terms of an arithmetic progression is 18
and the sum of the first four terms is 52. find the sum of the first eight terms

Can you guys help me please?

Thanks Allot
Peder

User avatar
stapel_eliz
Posts: 1734
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Thu Jun 18, 2009 11:22 pm

By definition of arithmetical sequences, the sum of the first four terms is the sum of the first two, plus two more copies of the common difference "d":

52 = 18 + 2d

What then is the value of "d"? Then what will be the value of the first eight terms, being the sum of the first four, plus another four copies of the common difference? :wink:

User avatar
Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

Re: Sequences: sum of 1st 2 terms is 18, sum of 1st 4 is 52

Postby Martingale » Fri Jun 19, 2009 1:13 am

pederjohn wrote:Well i am now totally lost...

I want so to solve this maths problem on my own but i have no idea how to solve it... I can solve it the long way but how can i do it quicker?

Code: Select all

The sum of the first two terms of an arithmetic progression is 18
and the sum of the first four terms is 52. find the sum of the first eight terms

Can you guys help me please?

Thanks Allot
Peder


to start off, you should be able to create a system of two equations and two unknowns.


Return to “Discrete Math”