Question

sum of certain sum of certain consecutive odd numbers starting from 1 is 324 how many odd numbers are added ​

Answer 1

Answer:

Here ;

sum of consecutive odd numbers = (S) = 324

first term = a = (t1) = 1

difference between two consecutive odd numbers = (d) = 5-3 = 3-1 = 2

no. of odd numbers added = n

Formula for a sum of consecutive odd numbers =

2S = n*[ 2a + (n-1)d]

2*(324) = n*[2*(1) + (n-1)*2 ]

628 = n* [2*(1)+ (n-1)*2]

628 = n* [2 (1+n-1)] ....(Taking 2 common in RHS)

628 = n*2*(n)

628 = 2n²

Divide both sides by 2

324 = n²

Taking Square-root both sides

18 = n

i.e. n = 18

Therefore 18 odd numbers are added for getting sum 324.