Final answer:
To find the sum of 10 consecutive integers, we can use the formula for the sum of an arithmetic series. One possible set of integers that satisfy the given sum is 169, 173, 177, 181, 185, 189, 193, 197, 201, and 205.
Step-by-step explanation:
To find the sum of 10 consecutive integers, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is given by the formula 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. In this case, we have 10 terms and the sum is 1738, so we can set up the equation 1738 = (10/2)(2a + (10-1)d).
Simplifying the equation, we have 1738 = 5(2a + 9d). We can then divide both sides of the equation by 5 to get 347.6 = 2a + 9d.
From here, we can use trial and error or substitution to find the values of a and d that satisfy the equation. One possible set of values that satisfy the equation is a = 169 and d = 4. Therefore, the 10 consecutive integers are 169, 173, 177, 181, 185, 189, 193, 197, 201, and 205.