How many elements are there in the set A = {2, 4, 6, ..., 50}?
Answer and explanation
Correct answer: 25
The set contains all positive even numbers from 2 through 50. These can be written as 2 × 1, 2 × 2, ..., 2 × 25, so each integer from 1 to 25 gives exactly one element. Alternatively, for an arithmetic sequence, the number of terms is (last term − first term) ÷ common difference + 1 = (50 − 2) ÷ 2 + 1 = 25. Hence the set has 25 elements.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The set contains all positive even numbers from 2 through 50. These can be written as 2 × 1, 2 × 2, ..., 2 × 25, so each integer from 1 to 25 gives exactly one element. Alternatively, for an arithmetic sequence, the number of terms is (last term − first term) ÷ common difference + 1 = (50 − 2) ÷ 2 + 1 = 25. Hence the set has 25 elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
