# Arithmetic Sequence with two variables

#### Lunatic

This is the question:

Given the sequence a+b, 2a-b, 3a-3b,_,_,_,_,8a-13b, insert four arithmetic sequence.

I can do it if it only has one variable, but our teacher hasn't taught us this. Please help

#### HallsofIvy

MHF Helper
I presume you mean four terms of an arithmetic sequence rather than "four arithmetic sequence".

Surely your teacher has taught you what an "arithmetic sequence" is! An arithmetic sequence always has the property that the difference between two consecutive terms is the same. You are given the first two terms, a+ b and 2a- b. Their difference is (2a- b)- (a+ b)= a- 2b. The next term is given as 3a- 3b. The difference between the third and second terms is (3a- 3b)- (2a- b)= a- 2b also! So we know the "constant difference" is a- 2b. The fourth term must be the third term 3a- 3b plus that constant difference, 3a- 3b+ (a- 2b). What is that? Can you now find the fifth, sixth, seventh, and eighth terms? Finally, as a check add a- 2b to the eighth term to verify that you get 8a- 13b.

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#### Lunatic

She must have typed a typo. I got the answer now, thank you.

#### Lunatic

I misunderstood the question. I assumed that the teacher was as also asking for the value of a and b as well. When all she asked for was the next 4 arithmetic terms. Thanks again