Question

02.25.17
Q 76/100 If the sum of five numbers in
A.P. is 25 and the sum of their squares is
165, then difference between the maximum
and minimum number is​

Answer 1

Answer:

Step-by-step explanation:

Let the numbers in A.P be a-2d, a-d, a, a+d, a+2d

Now ATQ

a-2d+a-d+a+a+d+a+2d=25

5a=25

a=5

ALSO IT IS GIVE THAT

(a-2d) ^2+(a-d) ^2+a^2+(a+d) ^2+(a+2d) ^2=165

a^2+4d^2-4ad+a^2+d^2-2ad+a^2+a^2+d^2+2ad+a^2+4d^2+4ad=165

5a^2+10d^2=165 [simplified version]

5(5) ^2+10d^2=165 [a=5 calculated above]

10d^2=165-125

d^2=40/10

d^2=4

d=+-2

So the numbers are by putting value of a and d in the assumed numbers above (a-2d, a-d......)

Numbers are 1,3,5,7,9 in both cases whether you put d=-2or d=+2

Maximum number=9

Minimum number=1

So their difference is 8 answer