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
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The common difference is x-y
:
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!!!
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:
