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Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11,… , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23,…. Then, the number of elements in the set X ∪ Y is _____.
Correct answer is '3748'. Can you explain this answer?
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Let Xbe the set consisting of the first 2018 terms of thearithmetic pr...
Explanation:
Given Arithmetic Progressions:
- X: 1, 6, 11, ...
- Y: 9, 16, 23, ...
Finding the Number of Terms in X and Y:
- The nth term of an arithmetic progression is given by:
a + (n-1)d, where a is the first term and d is the common difference.
- For X: a = 1, d = 5
The 2018th term of X = 1 + (2018-1) * 5
= 10085
- For Y: a = 9, d = 7
The 2018th term of Y = 9 + (2018-1) * 7
= 14113
Finding the Number of Elements in X ∪ Y:
- The union of two sets includes all unique elements from both sets.
- Since both X and Y have 2018 terms, we have to find the number of unique terms in X ∪ Y.
- The number of unique terms in X ∪ Y is the sum of the number of terms in X and Y minus the number of terms they have in common.
- To find the number of terms they have in common, we need to find the number of terms in the intersection of X and Y.
- The nth term of X: 1 + (n-1)5 = 1 + 5n
- The nth term of Y: 9 + (n-1)7 = 9 + 7n
- Setting the two equations equal gives: 1 + 5n = 9 + 7n
- Solving for n gives n = 4
- Therefore, the number of terms in the intersection of X and Y is 1.
- So, the number of elements in X ∪ Y = 10085 + 14113 - 1 = 24297
Therefore, the number of elements in the set X ∪ Y is 24297.
Given Arithmetic Progressions:
- X: 1, 6, 11, ...
- Y: 9, 16, 23, ...
Finding the Number of Terms in X and Y:
- The nth term of an arithmetic progression is given by:
a + (n-1)d, where a is the first term and d is the common difference.
- For X: a = 1, d = 5
The 2018th term of X = 1 + (2018-1) * 5
= 10085
- For Y: a = 9, d = 7
The 2018th term of Y = 9 + (2018-1) * 7
= 14113
Finding the Number of Elements in X ∪ Y:
- The union of two sets includes all unique elements from both sets.
- Since both X and Y have 2018 terms, we have to find the number of unique terms in X ∪ Y.
- The number of unique terms in X ∪ Y is the sum of the number of terms in X and Y minus the number of terms they have in common.
- To find the number of terms they have in common, we need to find the number of terms in the intersection of X and Y.
- The nth term of X: 1 + (n-1)5 = 1 + 5n
- The nth term of Y: 9 + (n-1)7 = 9 + 7n
- Setting the two equations equal gives: 1 + 5n = 9 + 7n
- Solving for n gives n = 4
- Therefore, the number of terms in the intersection of X and Y is 1.
- So, the number of elements in X ∪ Y = 10085 + 14113 - 1 = 24297
Therefore, the number of elements in the set X ∪ Y is 24297.
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Let Xbe the set consisting of the first 2018 terms of thearithmetic pr...
Correct answer is'3748'
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Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?
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Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let Xbe the set consisting of the first 2018 terms of thearithmetic progression 1, 6, 11,… , and Ybe the set consistingof the first 2018 terms of the arithmetic progression 9, 16, 23,….Then, the number of elements in the set X∪ Y is _____.Correct answer is '3748'. Can you explain this answer?.
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