It seems that you’ve uploaded an image. Let me first analyze its contents to understand the mathematical problem you're referring to. PIL import Image

Load the image to analyze

img_path = '/mnt/data/1733464904259h2uehv19.jpg' img = Image.open(img_path)

Display the image to understand its contents

img.show()I have displayed the image you uploaded. Let me extract and analyze the contents to assist you with your mathematical query. I will now proceed to interpret it. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(img)

extracted_textThe image contains a problem related to an arithmetic sequence, specifically asking to find values for $a_g$ and $a_n$ based on the sequence $2, 6, 10, \dots$. It also asks for the general form of the nth term, which is typically written as $a_n = bn + a$.

Let’s break this down:

1. Sequence Given: $2, 6, 10, \dots$

   • The first term $a_1 = 2$.
   • The common difference $d = 6 - 2 = 4$.

2. General Formula for Arithmetic Sequence: The nth term of an arithmetic sequence can be written as: $a_n = a_1 + (n - 1) \cdot d$ Plugging in the values: $a_n = 2 + (n - 1) \cdot 4 = 2 + 4n - 4 = 4n - 2$

Thus, the general term is $a_n = 4n - 2$.

Now, to find $a_g$ and $a_n$:

• $a_g$ and $a_n$ likely refer to specific terms in the sequence, and we'd need more context on what "g" and "n" represent. If $g$ is a specific term index, you can substitute that into the formula $a_n = 4n - 2$ to find its value.

Would you like to proceed with specific values for $g$ or $n$, or would you like further explanation? Let me know how I can assist you further!

Related Questions:

1. What is the nth term for a sequence where the first term is 3 and the common difference is 5?
2. How do you identify the common difference in an arithmetic sequence?
3. How can we derive the general formula for an arithmetic sequence from its first few terms?
4. What is the difference between arithmetic and geometric sequences?
5. How can we find the sum of the first $n$ terms in an arithmetic sequence?

Tip:

When working with arithmetic sequences, always remember that the common difference is constant, and you can find the general term by using the formula $a_n = a_1 + (n-1) \cdot d$.