SOLUTION: What position (n) in the sequence is the following? tn = 680 t1 = 104 d = 16

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Question 1162982: What position (n) in the sequence is the following?
tn = 680
t1 = 104
d = 16
Answer by ikleyn(52787)   (Show Source):
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.

I will assume, based on the context and designations, that      is an arithmetic progression.

Then the distance on the number line from the first to the last term is 680-104 = 576, and the number of intervals (gaps) between

the first and the last terms is    = 36.

Hence, the number 680 is the 37-th term of the sequence.

ANSWER.   n = 37.

Solved.

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My lessons on arithmetic progressions in this site are
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
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    - Free fall and arithmetic progressions
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    - Increments of a quadratic function form an arithmetic progression
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
    - Calculating partial sums of arithmetic progressions
    - Finding number of terms of an arithmetic progression (*)
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    - Math Olympiad level problem on arithmetic progression
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The most relevant to your problem is the lesson marked (*) in the list.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Arithmetic progressions".