Question

Find 5number in a AP whose sum is 25and the sum of square is 135

Answer 1

Answer:

Five numbers are

3 ,4 , 5 , 6 & 7

Step-by-step explanation:

Let say 5 number of an AP are

a-2d , a-d , a , a+d , a+2d

Sum of 5 numbers

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

= 5a

Sum = 25

=> 5a = 25

=> a = 5

so 5 terms

5-2d , 5-d , 5 , 5+d , 5+2d

Sum of squared of these numbers

= (5-2d)² + (5-d)² + 5² + (5+d)² + (5+2d)²

= 25 + 4d² - 20d + 25 + d² -10d + 25 + 25 + d² + 10d + 25 + 4d² + 20d

= 125 + 10d²

Sum of square of numbers given = 135

=> 125 + 10d² = 135

=> 10d² = 10

=> d² = 1

=> d = ± 1

Putting d = 1

numbers are  3 , 4 ,5 , 6 , 7

Putting d = -1

Numbers are 7 , 6 , 5 , 4 , 3