What is the sum of the first 700 consecutive odd numbers?
sum of arithmetic series
a1 = 1
d = 2
an = a1 + (n-1) d
so
a700 = a1 +(699)(2)
sum = (a1 + a700)/n
To find the sum of the first 700 consecutive odd numbers, we can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = (n/2) * (2a + (n-1)d)
Where:
S is the sum of the series,
n is the number of terms in the series,
a is the first term of the series, and
d is the common difference between the terms of the series.
In this case, the first term, a, is 1, the common difference, d, is 2 (since consecutive odd numbers have a difference of 2), and the number of terms, n, is 700.
Let's plug these values into the formula to find the sum:
S = (700/2) * (2(1) + (700-1)(2))
= 350 * (2 + 699(2))
= 350 * (2 + 1398)
= 350 * 1400
= 490,000
Therefore, the sum of the first 700 consecutive odd numbers is 490,000.