What is the sum of the first 1400 consecutive odd numbers?

Answer 1

The sum of the first 1400 odd numbers is 1960000.

The sum of an arithmetic progression is given by:

sum = n/2 (2a + (n-1)d)

where n is the number of items (in this case n = 1400)

where a is the first number (in this case a = 1)

where d is the common difference between terms (in this case d = 2)

Thus:

sum = 1400/2 × (2×1 + (1400 - 1)×2)

→ sum = 1400/2 × 2(1 + 1400 - 1)

→ sum = 1400 × 1400 = 1960000