SOLUTION: The third term of an a.p is 4x-2y and the 9th term is 10x -8y.find the common difference

Question 1150756: The third term of an a.p is 4x-2y and the 9th term is 10x -8y.find the common difference
Found 3 solutions by rothauserc, MathTherapy, greenestamps:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
the formula for the nth term of an arithmetic progression is
:
a(n) = a +d(n-1), where a is the first term and d is the common displacement
:
we are given
:
a(3) = a+d(3-1) = 4x-2y
:
a(9) = a+d(9-1) = 10x-8y
:
solve each equation for a and then set them equal to each other
:
a +2d = 4x -2y
:
1) a = 4x -2y -2d
:
a +8d = 10x -8y
:
2) a = 10x -8y -8d
:
4x -2y -2d = 10x -8y -8d
:
-2d = 6x -6y -8d
:
6d = 6x -6y
:
d = x -y
:
The common difference is x-y
:
Answer by MathTherapy(10806)   (Show Source): You can put this solution on YOUR website!
The third term of an a.p is 4x-2y and the 9th term is 10x -8y.find the common difference

Being an A.P., we get:
----- Substituting 3 for n
------ Substituting 4x - 2y for ----- eq (i)

------ eq (ii)
6x - 6y = 6d ------ Subtracting eq (i) from eq (ii)
6(x - y) = 6(d)

If you're learning SEQUENCES, the way I did the problem is the CORRECT way to do it. IGNORE that other person who believes that he's the only one on earth who knows how to do math.
In mathematics there are formulas that you have to learn, and he believes it's UNNECESSARY to learn and apply these formulas. AGAIN, IGNORE HIM!!!
Answer by greenestamps(13330)   (Show Source): You can put this solution on YOUR website!

Expressing the third and ninth terms in terms of the first term and common difference, as both the other tutors did, adds unnecessary steps (and time) to finding the solution.

The ninth term is the third term, plus 9-3=6 times the common difference:

RELATED QUESTIONS
5th term of an A.P is 9 and the 8th term is 27 find the 6th term and common difference... (answered by ikleyn)
if the 3rd term of an arithmetic sequence is 13 and the 9th term is 37, what is the... (answered by Edwin McCravy)
The fifth term of an arithmetic progression is three times the second term,and the third... (answered by ikleyn)
The first term of an arithmetic progression is -8. The ratio of the 7th term to the 9th... (answered by josgarithmetic)
the 6th term of a G.p is 1215. Given that the common ratio is 3, find the 9th... (answered by ewatrrr)
Find the 9th term of the geometric sequence whose first term is 2 and whose common ratio... (answered by MathLover1)
The sum of an AP is 4 and d first term is twice the third term of a GP,find (I)the 23rd... (answered by ikleyn)
An exponential sequence is such that the difference between the third term and the first... (answered by josgarithmetic)
In an arithmetic sequence, the sixth term is twice the third term and the 30th term is... (answered by josgarithmetic)