Question

Observe the following pattern
1 + 3 = 2²
1 + 3 + 5 = 3²
1 + 3 × 5 + 7 = 4²
and write the value of 1 + 3 + 5 + 7 + 9 + ... upto n terms.

Answer 1

From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ... n = n², where the left hand side consists of n terms.