The sum of 17 consecutive numbers is 289. The sum of another 10 consecutive numbers, whose first term is 5 more than the average of the first set of consecutive numbers, is:

Options

A. 30
B. 265
C. 285
D. 315

Answer

To solve the problem step by step, we will first find the average of the first set of 17 consecutive numbers and then use that to find the sum of the second set of 10 consecutive numbers.

### Step 1: Find the average of the first set of 17 consecutive numbers.
The sum of the 17 consecutive numbers is given as 289.

To find the average, we use the formula:
\[ \text{Average} = \frac{\text{Sum}}{\text{Number of terms}} = \frac{289}{17} \]

Calculating this gives:
\[ \text{Average} = \frac{289}{17} = 17 \]

### Step 2: Determine the first term of the second set of consecutive numbers.
The first term of the second set of 10 consecutive numbers is 5 more than the average of the first set.

So, we calculate:
\[ \text{First term of second set} = \text{Average} + 5 = 17 + 5 = 22 \]

### Step 3: Find the sum of the second set of 10 consecutive numbers.
The first term of the second set is 22. The 10 consecutive numbers starting from 22 are:
22, 23, 24, 25, 26, 27, 28, 29, 30, 31.

To find the sum of these numbers, we can use the formula for the sum of an arithmetic series:
\[ \text{Sum} = \frac{n}{2} \times (\text{First term} + \text{Last term}) \]
where \( n \) is the number of terms.

Here, \( n = 10 \), the first term is 22, and the last term is 31.

Calculating the sum:
\[ \text{Sum} = \frac{10}{2} \times (22 + 31) = 5 \times 53 = 265 \]

### Final Answer:
The sum of the second set of 10 consecutive numbers is **265**.

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