Math Problem Statement
jawablah pertanyaan berikut
Solution
The problem you shared is about solving for terms in an arithmetic sequence (barisan aritmetika). Let's break down the problem:
Given Information:
- The third term () of an arithmetic sequence is .
- The eighth term () is .
Questions:
- Find the first term () and the common difference () of the sequence.
- Find the general formula for the -th term ().
- Determine the 20th term ().
- Find the value of such that .
Step-by-Step Solution:
1. Finding and
The general formula for the -th term of an arithmetic sequence is: For , we have: For , we have:
Now, solve this system of equations:
Subtract equation (1) from equation (2):
Now substitute into equation (1):
Thus, the first term and the common difference .
2. General Formula for
Now that we have and , the general formula for the -th term is:
3. Finding the 20th Term
Using the general formula , we substitute :
Thus, the 20th term is .
4. Finding such that
Set in the general formula and solve for :
Thus, .
Final Answers:
- First term () = 5, common difference () = 3.
- General formula: .
- 20th term () = 62.
- when .
Would you like any more details or have further questions?
Here are 5 related questions:
- How do you find the sum of the first terms of an arithmetic sequence?
- What happens to the arithmetic sequence if the common difference is negative?
- How would you determine if a sequence is arithmetic or geometric?
- Can an arithmetic sequence have non-integer terms? How?
- How do you find the common difference if you're only given non-consecutive terms?
Tip: In arithmetic sequences, the difference between consecutive terms is always constant, which makes it easier to identify and calculate other terms in the sequence.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Algebra
Formulas
U_n = a + (n-1)d
Theorems
-
Suitable Grade Level
Grades 7-9
Related Recommendation
Find a1, d, and nth Term of Arithmetic Sequence: 3rd Term = 16, 11th Term = 72
Find the 25th Term of an Arithmetic Sequence with First Term 3 and Fifth Term 11
Arithmetic Sequence: Find nth Term and 100th Term of 19, 15, 11, 7
Find the 11th Term of an Arithmetic Sequence
Find the 11th Term of an Arithmetic Sequence with nth Term 5n