Math Problem Statement
Solution
Let's break down the two problems shown in the image:
Problem 1:
"Enter A, B, C, D or E (when the correct answer is not in the choices)"
The sequences given are:
- A. 3, 6, 12, 24, ...
- B. 3, 6, 12, 24
- C. 5, -5, -15, -25,...
- D. 5, 10, 15, 20,...
This appears to be a question about sequences or progressions:
- A seems to follow a geometric sequence (multiply by 2): .
- B is the same as A, but stops at 24, so it's incomplete.
- C follows an arithmetic progression with a common difference of -10: .
- D follows an arithmetic progression with a common difference of 5: .
Problem 2:
"Enter A, B, C, D or E (when the correct answer is not in the choices)"
The sequences given are:
- A. 2x, 4x, 6x, 8x
- B. 2x, 0, -2x, -4x, ...
- C.
- D.
These sequences involve algebraic expressions:
- A is an arithmetic sequence with a common difference of .
- B is also an arithmetic sequence, but it alternates between positive and negative terms with a common difference of .
- C is a geometric progression where the power of increases by 2 each time.
- D is a linear sequence where each term increases by 2.
Let me know if you'd like further clarification or if you have any questions!
Do you want further details? Here are 5 follow-up questions:
- What is the formula for the nth term in an arithmetic sequence?
- Can you identify the common ratio in a geometric sequence?
- How would you calculate the sum of an arithmetic progression?
- What is the general term for a geometric sequence?
- How can you identify whether a sequence is arithmetic or geometric?
Tip: In arithmetic sequences, the difference between consecutive terms remains constant.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Progression
Geometric Progression
Algebraic Sequences
Formulas
Arithmetic progression nth term: a_n = a_1 + (n - 1) * d
Geometric progression nth term: a_n = a_1 * r^(n - 1)
Theorems
Arithmetic Sequence
Geometric Sequence
Suitable Grade Level
Grades 9-10
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