Question) Sum of the first n positive odd integers is 576. What is n?

Question

-- is the answer to this question n=24?

Answer 1

S_n = n[2a₁ + (n - 1)d] / 2, where S = sum, a₁ = first term, n = number of terms, d = common difference.

 

576 = n[2 + ( n - 1)2] /2

1152 = n[2 + 2n - 2]

1152 = n(2n)

1152 = 2n²

576 = n²

±24 = n

 

Only the positive number makes sense.

 

Yes, the sum of 24 terms is 576.