Final answer:
The sum of multiples of 3 from 15 to 45 is 225. This can be calculated by directly adding the multiples or by using the formula for the sum of an arithmetic sequence. The final total reflects the sum of this arithmetic series.
Step-by-step explanation:
The correct answer to the question is b. 225.The multiples of 3 between 15 and 45 are 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, and 45. To find the sum of thesenumbers, you can simply add them together: 15 + 18 + 21 + 24 + 27 + 30 + 33 + 36 + 39 + 42 + 45 = 225. Alternatively, you can notice this is an arithmetic sequence, where you can use the formula for the sum of an arithmetic series S = n/2(a1 + an), where n is the number of terms, a1 is the first term and an is the last term. In this case, a1 is 15, an is 45, and the common difference is 3, thus the number of terms n is (an - a1) / d + 1 = (45 - 15) / 3 + 1 = 11. Applying the formula, we get S = 11/2(15 + 45) = 11/2 * 60 = 330/2 = 165.
The sum of the multiples of 3 from 15 to 45 can be found by finding the number of terms in the sequence and then using the formula for the sum of an arithmetic series. The first term is 15 and the common difference is 3, so the last term is 45. The number of terms can be found by subtracting the first term from the last term and dividing by the common difference, then adding 1. In this case, there are (45 - 15) / 3 + 1 = 11 terms. The sum can be found using the formula S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get S = (11/2)(15 + 45) = 11(60) = 660. Therefore, the sum of multiples of 3 from 15 to 45 is 660.