Final answer:
To find the sum of all two-digit numbers that leave a remainder of 1 when divided by 3, use the arithmetic sequence formula.
Therefore, the correct answer is a. 1616.
Step-by-step explanation:
To find the sum of all two-digit numbers that leave a remainder of 1 when divided by 3, we can use the arithmetic sequence formula.
The formula for the nth term of an arithmetic sequence is a + (n - 1)d, where a is the first term, n is the number of terms, and d is the common difference.
In this case, the first term is 10 and the common difference is 3. Let's find the number of terms in the sequence:
(last term - first term) / common difference + 1 = (99 - 10) / 3 + 1 = 90 / 3 + 1 = 30 + 1 = 31
Now, let's find the sum of the sequence:
(n / 2)(first term + last term) = (31 / 2)(10 + 99) = 15.5 * 109 = 1694.5
The sum of all two-digit numbers that leave a remainder of 1 when divided by 3 is 1694.5.