Final answer:
The sum of the first 42 terms of the arithmetic sequence starting with 5 and with a common difference of 3 is 2793.
Step-by-step explanation:
The student wants to find the sum of the first 42 terms of an arithmetic sequence. The sequence provided is 5, 8, 11, 14, 17, which indicates that the common difference (d) between the terms is 3. To find the sum of the first 42 terms, we can use the formula for the sum of an arithmetic series: Sn = n/2(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.
For this sequence, a=5, n=42, and d=3. So, the sum would be S42 = 42/2(2*5 + (42-1)*3), which simplifies to S42 = 21(10 + 123) = 21*133 = 2793. Therefore, the sum of the first 42 terms is 2793.