SOLUTION: Please help me. 2p+3, 4p+3, and 5p+2 are the first three terms in an arithmetic sequence. How to find p? Thank you.

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Question 1112962: Please help me. 2p+3, 4p+3, and 5p+2 are the first three terms in an arithmetic sequence. How to find p?
Thank you.
Found 2 solutions by ikleyn, rothauserc:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
If three numbers a%5B1%5D, a%5B2%5D  and  a%5B3%5D form an arithmetic progression, then

a%5B3%5D - a%5B2%5D = a%5B2%5D - a%5B1%5D,


by the definition of an arithmetic progression.


It gives you an equation, in your case,


(5p+2) - (4p+3) = (4p+3) - (2p+3).


Simplify and solve for "p".


Then, having "p", restore the three numbers.

----------------
On arithmetic progressions, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


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 rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
the formula for the nth term of an arithmetic sequence is
:
x(n) = a + d(n-1), where a is the first term and d is the common difference
:
x(1) = a + d(1-1) = a, therefore
:
a = 2p +3
:
we see that the second term ( x(2) ) is
:
4p +3 = 2p +3 +d
:
solve for d
:
d = 2p
:
x(3) is
:
5p +2 = 2p +3 +2p(2)
:
solve for p
:
5p +2 = 6p +3
:
*******
p = -1
*******
:
therefore, a=1, d=-2 and the sequence is
:
1, -1, -3
: