Final answer:
The sum of the first 100 terms is 40,400.
Step-by-step explanation:
To find the sum of the first 100 terms, we need to find the pattern in the given numbers. The given numbers seem to be increasing by 8 each time. So, we can create an arithmetic sequence with a common difference of 8. The formula to find the sum of an arithmetic sequence is:
S = (n/2)(2a + (n-1)d)
where S is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, a = 8, d = 8, and n = 100, we get:
S = (100/2)(2(8) + (100-1)(8)) = 50(16 + 99(8)) = 50(16 + 792) = 50(808) = 40,400.