SOLUTION: Arithmetic Series Question: Determine the number of terms in the following arithmetic sequence. 2x + y, 3x + 4y, 4x + 7y,...10x + 25y Textbook answer is 10. Can someone p

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Question 1192001: Arithmetic Series Question:
Determine the number of terms in the following arithmetic sequence.
2x + y, 3x + 4y, 4x + 7y,...10x + 25y
Textbook answer is 10.
Can someone please tell me how to get 10? Thank you.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Checking for the difference from each term to each index+1 term , using your first three terms will show that each next term is found by adding x+3y.
...
..

9 terms in your given sequence.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Arithmetic Series Question:
Determine the number of terms in the following arithmetic sequence.
2x + y, 3x + 4y, 4x + 7y,...10x + 25y
Textbook answer is 10.
Can someone please tell me how to get 10? Thank you.
10 is WRONG.

Let's JUST use each term's 1st expression to get m=number of terms.
1st term's first expression: 2x
2nd term's first expression: 3x
3rd term's first expression: 4x
It's quite clear that d (DIFFERENCE) in terms ix x

Again, using JUST the 1st expression of each term, and applying the number-of-terms formula:
, we get: 

You could also LIST all terms, although this involves a little bit more work!

Don't know how an answer of 10 terms was derived!

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