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प्रश्न
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
उत्तर
Here, we are given that four number are in A.P., such that there sum is 50 and the greatest number is 4 times the smallest.
So, let us take the four terms as a - d, a, a +d, a + 2d.
Now, we are given that sum of these numbers is 50, so we get,
(a - d) + (a) + (a + d) + (a + 2d) = 50
a - d + a + a + d + a + 2d = 50
4a + 2d = 50
2a + d = 25 .....(1)
Also the greatest number is 4 times the smallest so we get
a + 2d = 4(a - d)
a + 2d = 4a - 4d
4d + 2d = 4a - a
6d = 3a
`d = 3/6 a` .....(2)
Now using (2) in (1) we get
`2a + 3/6 a = 25`
`(12a + 3a)/6 = 25`
15a = 150
`a = 150/15`
a = 10
Now using the value of a in (2) we get
`d = 3/6 (10)`
`d = 10/2`
d = 5
So first term is given by
a - d = 10 - 5
= 5
Second term is given by
a = 10
Third term is given by
a + d = 10 + 5
= 15
Fourth term is given by
a + 2d = 10 + (2)(5)
= 10 + 10
= 20
Therefore the four terms are 5, 10, 15, 20
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