Find the sum of the first 35 consecutive odd numbers.
What is the sum of the first 350 consective odd numbers?
sum of first n odd numbers is n^2
To find the sum of consecutive odd numbers, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(2a + (n-1)d)
where:
n is the number of terms in the series,
a is the first term of the series, and
d is the common difference between consecutive terms.
For the first 35 consecutive odd numbers, n = 35 and a = 1 (since the first odd number is 1), and d = 2 (since the difference between consecutive odd numbers is 2).
Substituting these values into the formula, we have:
Sum = (35/2)(2(1) + (35-1)(2))
= (35/2)(2 + 34*2)
= (35/2)(2 + 68)
= (35/2)(70)
= 35 * 35
= 1225
So, the sum of the first 35 consecutive odd numbers is 1225.
To find the sum of the first 350 consecutive odd numbers, we can use the same formula. Now, n = 350, a = 1, and d = 2. Substituting these values into the formula, we have:
Sum = (350/2)(2(1) + (350-1)(2))
= (350/2)(2 + 349*2)
= (350/2)(2 + 698)
= (350/2)(700)
= 350 * 350
= 122500
Therefore, the sum of the first 350 consecutive odd numbers is 122500.