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Home » Find the 4 numbers in A.P., whose sum is fifty and in which the greatest number is four times the least.
Find the 4 numbers in A.P., whose sum is fifty and in which the greatest number is four times the least.
Arithmetic Progressions | CBSE | Class 10 | Maths | RD Sharma
Find the 4 numbers in A.P., whose sum is fifty and in which the greatest number is four times the least.

Let’s take the four terms of the A.P. to be (a-3d), (a-d), (a+d) and (a+3d).

According to the question,

Sum of those terms =50

⇒ (a-3d)+(a-d)+(a+d)+(a+3d)=50

⇒ a-3d+a-d+a+d+a-3d=50

⇒ 4a=50

⇒ a=50/4=25/2

also given that the greatest number =4\times least number

⇒ a+3d=4(a-3d)

⇒ a+3d=4a-12d

⇒ 4a-a=3d+12d

⇒ 3a=15d

⇒ a=5d

By Using the value of a in the above equation, we get

⇒ 25/2=5d

⇒ d=5/2

Therefore,the terms will be:

(a-3d)=(25/2-3(5/2)), (a-d)=(25/2-5/2), (25/2+5/2) and (25/2+3(5/2)).

⇒ 5, 10, 15, 20

i

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