If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are

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Here, we are given that four numbers are in A.P., such that their 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 6 d = 3a d = $\frac{3}{6}$ a ....................(2) Now, using (2) in (1), we get, 2a + $\frac{3}{6}$ a = 25 (12a + 3a)/6 = 25 15a = 150 a = $\frac{150}{15}$ a = 10 Now, using the value of a in (2), we get, d = $\frac{3}{6}$ (10) d = $\frac{10}{2}$ 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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