https://file.aiquickdraw.com/mathbot/file/1727324344062i4wsmdo8.jpg

In the uploaded image, you're dealing with an arithmetic sequence where you have the following terms and differences:
- \( u_1 \) (first term)
- \( u_2 = u_1 + d \)
- \( u_3 = u_1 + 2d \)
- \( u_2 - u_1 = 12 \)
- \( u_3 - u_2 = 21 \)

From the equations given:
- \( u_2 - u_1 = d = 12 \)
- \( u_3 - u_2 = d = 21 \)

However, these differences should be the same in an arithmetic sequence, implying there might be an error in the problem statement or in the interpretation of \( u_3 \). Assuming the second difference is a mistake and the common difference is 12 (based on \( u_2 - u_1 \)), we can then calculate the first term \( u_1 \) as follows:

1. From the problem, we know \( u_3 = u_1 + 2d = 30 \).
2. Substitute \( d = 12 \) into \( u_3 = u_1 + 24 \).
3. Solve \( u_1 + 24 = 30 \) to find \( u_1 \).

Let's solve for \( u_1 \) now.

An arithmetic sequence has u1 = 12, u2 = 21, u3 = 30. Find the common difference d, find u10, and find S10.

Learn how to find the common difference, the 10th term, and the sum of the first 10 terms in an arithmetic sequence with u1 = 12, u2 = 21, and u3 = 30. Step-by-step solution provided for high school math students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation