A rocket rises 30 feet after 1 second, 85 feet after 2 second, and 140 feet after 3 seconds. If it continues to rise at this rate, how many feet will it rise after 16 seconds?
A.780 ft
B.830 ft
C.855 ft
D.910 ft

To solve the problem, we can first determine the pattern of the rocket's rise by finding the common differences between consecutive heights.

Given heights:
- After 1 second: 30 feet
- After 2 seconds: 85 feet
- After 3 seconds: 140 feet

### Step 1: Find the first differences (differences between consecutive heights):
- Difference between 2nd and 1st: \( 85 - 30 = 55 \) feet
- Difference between 3rd and 2nd: \( 140 - 85 = 55 \) feet

The first difference is constant, which suggests that the rocket is rising at a constant rate of 55 feet per second after the first second.

### Step 2: Find the height at 16 seconds
Since the height increases by 55 feet every second after the first second, we can use the following equation:

\[
\text{Height after } n \text{ seconds} = \text{Initial height} + (n - 1) \times \text{Common difference}
\]

Where:
- Initial height = 30 feet
- Common difference = 55 feet
- \( n = 16 \) seconds

\[
\text{Height after 16 seconds} = 30 + (16 - 1) \times 55 
\]

\[
\text{Height after 16 seconds} = 30 + 15 \times 55
\]

\[
\text{Height after 16 seconds} = 30 + 825
\]

\[
\text{Height after 16 seconds} = 855 \text{ feet}
\]

Thus, the correct answer is **C. 855 feet**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the common difference in an arithmetic sequence?
2. Can you derive a formula for the nth term of an arithmetic sequence?
3. How do you determine whether a sequence is arithmetic?
4. What if the common difference was not constant—how would that affect the calculation?
5. How does the concept of arithmetic sequences apply in real-world scenarios?

**Tip:** Always check if the differences between terms are constant when identifying an arithmetic sequence.

Explore how to calculate the height of a rocket after 16 seconds using arithmetic sequences. Learn about the constant rate of change and solve similar problems with step-by-step explanations. Suitable for Grades 6-8 students.

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