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

[pederjohn]

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

[stapel_eliz]

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?

[Martingale]

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.

[bigj]

therefore, 2a+d=18
and 4a+6d=52
solving, a=7,d=4;
therefore sum=(8/2)*(2*7+(8-1)*4)=168,the ans.