Podcast
Questions and Answers
What are the three numbers in arithmetic progression (A.P.) whose sum is 18 and product is 192?
What are the three numbers in arithmetic progression (A.P.) whose sum is 18 and product is 192?
The sum of three consecutive terms of an A.P. is 30 if the product of the extremes is 120.
The sum of three consecutive terms of an A.P. is 30 if the product of the extremes is 120.
False
List the four numbers in A.P. such that their sum is 20.
List the four numbers in A.P. such that their sum is 20.
2, 4, 6, 8
The five numbers in A.P. whose sum is 25 can be represented as ______.
The five numbers in A.P. whose sum is 25 can be represented as ______.
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Match the following properties with their corresponding results in A.P.:
Match the following properties with their corresponding results in A.P.:
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Study Notes
Arithmetic Progression Problems
- Three numbers in A.P. have a sum of 18 and a product of 192.
- The solution yields the numbers 4, 6, and 8.
Consecutive Terms in A.P.
- For three consecutive terms that sum to 24 and have a product of two extremes equal to 55.
- The resulting terms are 5, 8, and 11.
Four Numbers in A.P.
- Four numbers must sum to 20 and the sum of their squares equals 120.
- The numbers found are 2, 4, 6, and 8.
Five Numbers in A.P.
- Five numbers total a sum of 25 and the sum of their squares is 135.
- The identified numbers are 3, 4, 5, 6, and 7.
Properties of A.P. Involving Variables
- If ( a, b, c ) are in A.P.:
- Show that ( \frac{a(b+c)}{bc}, \frac{b(c+a)}{ca}, \frac{c(a+b)}{ab} ) form an A.P.
- Demonstrate that ( a^2(b+c), b^2(c+a), c^2(a+b) ) are in A.P.
- Prove ( \frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab} ) are in A.P.
- ( b+c, c+a, a+b ) create an A.P.
- ( b+c-a, c+a-b, a+b-c ) also form an A.P.
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Description
This quiz focuses on long answer type questions related to arithmetic progression (A.P.). Students will find sums and products of numbers in A.P., explore relationships, and solve for unknowns based on given conditions. Perfect for mastering concepts in algebra for class 10.
