The sum of the first n positive odd integers is 64. Find n?

The sum of the first n positive odd integers is always n²

For example:
1 = 1²
1 + 3 = 2² = 4
1 + 3 + 5 = 3² = 9
1 + 3 + 5 + 7 = 4² = 16

(If you want to see it visually, check the image link below.)

Once you figure out that pattern, it is obvious that n = 8.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 8² = 64

Answer:
n = 8

The first n positive odd integers form an arithmetic sequence.
The first term, a₁ = 1
The common difference, d = 2

S(n) = 8
n [2a₁ + (n - 1)d] / 2= 64
n [2×1 + (n - 1)×2] = 128
n [2 + 2n - 2] = 128
2n² = 128
n² = 64
n = 8 or n = -8 (rejected)

Hence, n = 8

1, 3, 5, 7, ...
an = 2n - 1
Sn = n^2
n^2 = 64
n = 8

Happily, there's a simple formula for this:

The sum of the first n odd positive integers

is n^2. Here we're told n^2 = 64, so that is

the sum of the first 8 odd positive integers