Math Problem Statement
Solution
The image contains a math test on the topic of "Pola Bilangan" (Number Patterns) with a set of questions asking to solve pattern-based problems. Let's break them down:
1. Look at the configuration of the shapes.
- (a) Determine how many triangles are in pattern 10.
- (b) Find the formula for the -th term of this configuration.
2. A sequence is given: 1, 3, 6, 10, 15, 21, ...
- (a) Is this sequence an arithmetic sequence? Explain your reasoning.
3. A sequence is given: 36, 33, 30, 27, ...
- (a) Determine the 12th term of this sequence.
- (b) Find the formula for the -th term of this sequence.
- (c) Find the sum of the sequence up to the 12th term.
4. An arithmetic sequence is given with the 5th term as 31 and the 9th term as 59.
- (a) Determine the first term and the common difference of the sequence.
- (b) Find the 15th term of the sequence.
- (c) Find the sum up to the 15th term.
5. In an auditorium, there are 15 rows of seats. The first row has 18 seats, the second row has 21, and each subsequent row has 3 more seats than the previous.
- (a) Determine the number of seats in the last row.
- (b) Find the total number of seats in the entire auditorium.
6. A geometric sequence is given: 8, 4, 2, 1, ...
- (a) Find the next two terms.
- (b) Determine the 8th term.
7. A geometric sequence with the 3rd term as 6 and the 4th term as 9.
- Determine the ratio and the first term of the sequence.
8. An amoeba doubles every 15 minutes. If there are 3 amoebas at the start, calculate how many amoebas there will be after 2 hours.
Would you like help solving any of these specific problems, or should I explain the steps for all of them in detail?
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Geometric Progressions
Summation of Sequences
Pattern Recognition
Formulas
Arithmetic sequence formula: a_n = a_1 + (n-1)d
Geometric progression formula: a_n = a_1 * r^(n-1)
Sum of arithmetic series: S_n = (n/2) * (a_1 + a_n)
Sum of geometric series: S_n = a_1 * (1 - r^n) / (1 - r)
Theorems
Properties of arithmetic and geometric sequences
Summation Theorems for series
Suitable Grade Level
Grades 7-9
Related Recommendation
Solving Number Sequence Problems for Grades 7-9
Solving Sequences and Arithmetic Patterns in Mathematics
Identifying Patterns in Number Sequences - Arithmetic and Geometric Progressions
Pattern Recognition in Sequences: Solve Sequence Problems Easily
Step-by-Step Solutions to Arithmetic and Geometric Progression Problems