https://file.aiquickdraw.com/mathbot/file/17292382304416hmc01tv.jpg

The question on the image asks to create a new problem using a pattern in a sequence of numbers. It provides an example where the sequence is \( 1, 4, 7, \ldots \), and it asks for the 7th term in this sequence.

### Solution:
The given sequence \( 1, 4, 7, \ldots \) is an arithmetic sequence where each term increases by 3. The formula for the \( n \)-th term of an arithmetic sequence is:

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

where:
- \( a_1 \) is the first term,
- \( d \) is the common difference, and
- \( n \) is the term number.

For this sequence:
- \( a_1 = 1 \) (the first term),
- \( d = 3 \) (the common difference),
- \( n = 7 \) (we need to find the 7th term).

Plugging in the values:

\[
a_7 = 1 + (7 - 1) \cdot 3
\]

\[
a_7 = 1 + 6 \cdot 3
\]

\[
a_7 = 1 + 18
\]

\[
a_7 = 19
\]

### Answer:
The 7th term in the sequence is **19**.

Would you like a more detailed explanation or have any other questions about this? 

Here are 5 related questions:
1. How do you find the common difference in an arithmetic sequence?
2. What is the formula to find the sum of the first \( n \) terms of an arithmetic sequence?
3. How can we determine if a sequence is arithmetic or geometric?
4. How do you derive the formula for the \( n \)-th term of an arithmetic sequence?
5. Can you explain how to solve for \( n \) if you are given a term value in an arithmetic sequence?

**Tip:** Always check the common difference first when identifying the pattern in an arithmetic sequence. It helps in quickly determining the sequence's rule.

Menciptakan sebuah masalah baru menggunakan pola pada barisan bilangan. Misalnya, jika 1, 4, 7,... adalah barisan, berapa nilai ke-7?

Learn how to find the 7th term in the arithmetic sequence 1, 4, 7,... using the formula for the n-th term. This problem focuses on recognizing patterns in sequences and applying arithmetic sequence formulas, suitable for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation