Question

54. If the sum of first 'n' positive integers is 1/5 times
the sum of their squares then ‘n’equals to
(a) 8
(b) 9
(c) 7
(d) 12​

Answer 1

Answer:

If the sum of first n natural numbers is 1/5 times the sum of their squares, then the value of n is (1) 5 (2) 6 (3) 7 (4) 8. Given sum of the first n natural numbers is 1/5 times the sum of their squares. Hence option (3) is the answer.

Answer 2

Answer:

(c) n=7

Step-by-step explanation:

Sum of first n positive integers = n(n+1)/2

Sum of squares of n positive integers = n(n+1)(2n+1)/6

Now, it is given that sum of the first n positive integers is 1/5 times the sum of their squares.

So, n(n+1)/2 = (1/5)n(n+1)(2n+1)/6

15 = 2n+1

2n = 14

n = 7