Question

sum of three terms of an AP is 60 and sum of three squares is 1250.find middle term?

Answer 1

Answer:

Let the rational between three numbers be x

The ratio of 3 numbers is 3 : 4 : 5. This the three numbers are 3x, 4x and 5x.

The squares of the number is 9x^2, 16x^2 and 25x^2.

The sum of their squares is 1250. Accordingly

9x^2 + 16x^2 + 25x^2 = 1250

50x^2 = 1250

x^2 = 1250/50

x^2 = 25

x = √25

x = 5

The rational is 5, therefore the three numbers are

First number 3x = 3 × 5 = 15

Second number 4x = 4 × 5 = 20

Third number 5x = 5 × 5 = 25

Sum of the numbers = 15 + 20 + 25 = 60

Answer the sum of the numbers is 60 and the numbers are 15, 20 and 25