Math Problem Statement
The sum of three consecutive numbers of AP is33 and the product is 1287Then determine the numbers and also find the 7th and 14th terms
Solution
Let's solve the problem step by step.
Step 1: Define the three consecutive terms of the arithmetic progression (AP).
Let the three consecutive terms be , , and , where is the middle term and is the common difference.
Step 2: Use the sum of the three terms.
The sum of the three terms is given as 33: Simplifying this, we get:
Step 3: Use the product of the three terms.
The product of the three terms is given as 1287: Substitute : Simplify the equation: Divide by 11:
Step 4: Determine the three numbers.
If , the three numbers are , , and .
If , the three numbers would be , , and .
So, the three consecutive terms are , , and .
Step 5: Find the 7th and 14th terms of the AP.
The general term of the AP is given by: For and :
- The 7th term is:
- The 14th term is:
Final Answer:
- The three consecutive terms are 9, 11, and 13.
- The 7th term of the AP is 23.
- The 14th term of the AP is 37.
Would you like more details or have any questions?
Here are 5 related questions:
- What is the common difference in an arithmetic progression if the sum of three consecutive terms is given?
- How do you derive the general term of an arithmetic progression?
- What are the properties of the sum and product of terms in an arithmetic progression?
- How can you find the nth term of an arithmetic progression if the common difference is known?
- What is the formula for the sum of the first n terms of an arithmetic progression?
Tip: The product of terms in an arithmetic progression is often easier to work with by expressing terms around a middle term, especially when dealing with an odd number of terms.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Progression (AP)
Sum of terms in AP
Product of terms in AP
General term of AP
Formulas
General term of an arithmetic progression: \( a_n = a + (n-1) \cdot d \)
Theorems
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Suitable Grade Level
Grades 8-10
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