SOLUTION: find the first five terms of the arithmetic progression whose seventh and twenty-third terms are -5 and -29

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Question 1110572: find the first five terms of the arithmetic progression whose seventh and twenty-third terms are -5 and -29
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
HINT.  There is the room for 23 - 7 = 16 common differences between  -5  and  -29,


        which implies  d = %28%28-29%29-%28-5%29%29%2F16 = %28-29%2B5%29%2F16 = -24%2F16 = -3%2F2.


Based on it,  you can easily solve the problem to the end,  if you have elementary/introductory knowledge on arithmetic progressions.

If not,  then learn it from the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

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".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Sixteen common differences d from n=7 to n=23

-29-%28-5%29=-29%2B5=-24

General Term, A-%28n-1%29%2824%2F16%29, because the progression decreases.
A-%283%2F2%29%28n-1%29

A%5B7%5D=-5=A%5B1%5D-%283%2F2%29%287-1%29
.
A%5B1%5D=4

General Term more specifically is highlight%284-%283%2F2%29%28n-1%29%29;
Use that to find the values asked.