Question

Three numbers are in A.P their sum is 24 and sum of their square is 200.. Find the numbers??

Answer 1

Answer:

a=8 and d=±2

Step-by-step explanation:

Let a be the first term and d denote the common difference of the required A.P.

Let the numbers be in the form of a+d,a and a-d.

Given,

Sum of the numbers:24

Sum of the squares of the numbers:200

Now,

(a-d)+(a+d)+a=24

=>3a=24

=>a=8

Also,

a²+(a-d)²+(a+d)²=200

Putting a=8,

=>8²+(8+d)²+(8-d)²=200

=>64+(64+d²+16d)+(64+d²-16d)=200

=>2d²+192=200

=>2d²=200-192

=>2d²=8

=>d²=4

=>d= ±√4

=>d=±2= 2 or -2

Case 1: When d= -2

a-d,a,a+d,............

8-(-2),8,8+(-2)

10,8,6.............

Case 2: When d= 2

a-d,a,a+d,............

8-2,8,8+2,.........

6,8,10,.........

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