The image shows a question about an arithmetic sequence. Here's the content of the question:

Question 13:

The first 5 terms of an arithmetic progression (AP) are: $2, 5, 8, 11, 14$

Find the sum of the 8th and 9th terms:

A. 110
B. 218
C. 240
D. 158
E. 198

Let's solve this.

Step-by-step solution:

In an arithmetic progression (AP), the general term $a_n$ can be written as:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_1 = 2$ (first term)
• $d = 5 - 2 = 3$ (common difference)

Now, let's calculate the 8th and 9th terms.

• For $n = 8$: $a_8 = 2 + (8 - 1) \cdot 3 = 2 + 7 \cdot 3 = 2 + 21 = 23$

• For $n = 9$: $a_9 = 2 + (9 - 1) \cdot 3 = 2 + 8 \cdot 3 = 2 + 24 = 26$

The sum of the 8th and 9th terms is: $a_8 + a_9 = 23 + 26 = 49$

It seems the provided options do not match this value. Let me recheck.After calculating the 8th and 9th terms of the arithmetic progression, the sum is $23 + 26 = 49$, which doesn't match any of the options provided.

This may indicate an issue with the options listed, or there might be an alternative interpretation of the problem. If you'd like, we can recheck the terms or explore different aspects of the arithmetic progression to ensure everything is correct.

Do you want more details or have any further questions about this? Here are some related questions to explore:

1. How do we derive the formula for the $n$-th term in an arithmetic progression?
2. What are the main differences between arithmetic and geometric sequences?
3. How do you calculate the sum of the first $n$ terms of an arithmetic progression?
4. Can you find a way to solve this question using a recursive approach?
5. How would the solution change if the common difference were negative?

Tip: Always double-check your arithmetic sequences by recalculating the common difference and using the formula correctly.