Question

The ratio of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. The value of n is: a) 15 b) 25 c) 35 d) 40

Answer 1

Answer:

B) 25

Step-by-step explanation:

sum of squares of first n natural no's= n(n+1)(2n+1)/6

sq of sum of first natural no's=n(n+1) 2*n(n+1)/2

now the ratio is,

= n(n+1)(2n+1)/6:n(n+1)2*n(n+1)/2

= 17:325

thus, we get

n=25

Answer 2

Step-by-step explanation:

• So squares of sum of first n natural numbers is n(n + 1)/2 x n(n + 1)/2
• Now the ratio of these two has to be found by substituting the given values.
• Now n(n + 1)(2n + 1) / 6 : n(n + 1)/2 x n(n + 1)/2
• Values on n are 15,25,30 and 35
• So 15(15 + 1)(2(15) + 1)/6 : 15(15 + 1)/2 x 15(15 + 1)/2
•          15 x 16 x 31 / 6 : 15 x 16 / 2 x 15 x 16 / 2
•                   1240 : 14,400
•                     124 : 1440
•                         31 : 360 which is not the given ratio.
• Now substituting 25 we get
• So 25(25 + 1)(2(25) + 1)/6 : 25(25 + 1)/2 x 25(25 + 1)/2
•  25 x 26 x 51 /6 : 25 x 26 / 2 x 25 x 26 / 2
•        5525 : 105625
•           1105 : 21125
•             221 : 4225
•              17: 325 is the required ratio.

Reference link will be

https://brainly.in/question/49636806