Question

The sum of the n consecutive odd natural numbers
starting from 5 is 60. Find the value of (n²-n).
1. 20
2. 30
3. 42
4. 56​

Answer 1

Answer:

3. 30

Step-by-step explanation:

We have,

The AP - 5,7,9,11,13.....

First term 'a' = 5

Common Difference 'd' = 7-5 = 2

Sn = 60.

B/Q, n/2 [ 2a + (n-1)d ] = 60

=> n [ 2*5 + (n-1)*2 ] = 60*2

=> n ( 10 + 2n - 2 ) = 120

=> n ( 2n + 8 ) = 120

=> 2n² + 8n = 120

=> 2n² + 8n - 120 = 0

=> 2 ( n² + 4n - 60 ) = 0

=> n² + 4n -60 = 0/2

=> n² + ( 10 - 6 )n - 60 = 0

=> n² + 10n - 6n - 60 = 0

=> n ( n + 10 ) - 6 ( n + 10 ) = 0

=> ( n + 10 ) ( n - 6 ) = 0

=> Either ( n + 10 ) = 0 or ( n - 6 ) = 0

=> n + 10 = 0 => n - 6 = 0

=> n = -10 => n = 6

Since, n cannot be negative

Therefore, n is not equal to -10

Therefore, n = 6

Now,

( n² - n ) = (6)² - 6 = 36 - 6 = 30