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3a = 27
a = 9
The product of first and last is 56.
(a - d)(a + d) = 56
2
2
a - d = 56
2
2
9 - d = 56
2
d = 81 - 56 = 25
d = ± 5
Then the numbers are 4, 9, 14 or 14, 9, 4.
Example 6- The angles of a quadrilateral are in AP whose common difference is
10 degree. Find the angles.
Solution- Let the angles of the quadrilateral be X , X+10 . X+20 ,X+30
The sum of the angles of the quadrilateral = 360 degrees
X+ X+ 10 + X+20 +X +30 = 360
=> 4X +60 = 360
=>4X = 360 - 60 = 300
=> X = 75
The angles of the quadrilateral are 75, 85, 95, 105 degrees.
Example 7- Subba rao started work in1995 at annual salary of ₹5000 and received
an increment of ₹200 each year .in which year did his income reach ₹7000.
Solution- According to the condition,
5000, 5200, 5400 .... , 7000 forms an A.P since the difference between the consecutive
terms is 200.
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