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The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 is
- a)14
- b)21
- c)51
- d)28
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The number of terms common to the Arithmetic progressions 3, 7, 11, &#...
First A.P′s sequence is 3,7,11,....,407
General term will be 4k+3 k≤101
Second A.P's sequence is 2,9,16,....,709
General term will be 7p+2 p≤101
The common terms will be 51,79,...,28m + 51
28m + 51 ≤ 407
⟹ 28k ≤ 356
⟹ k ≤ 12.71
And adding the 2 starting number count of the 2 A.P′s i.e. 3 & 2
Number of common terms will be 12 + 2 = 14
General term will be 4k+3 k≤101
Second A.P's sequence is 2,9,16,....,709
General term will be 7p+2 p≤101
The common terms will be 51,79,...,28m + 51
28m + 51 ≤ 407
⟹ 28k ≤ 356
⟹ k ≤ 12.71
And adding the 2 starting number count of the 2 A.P′s i.e. 3 & 2
Number of common terms will be 12 + 2 = 14
Most Upvoted Answer
The number of terms common to the Arithmetic progressions 3, 7, 11, &#...
To find the number of terms common to the arithmetic progressions 3, 7, 11, ..., 407 and 2, 9, 16, ..., 709, we need to identify the terms that are present in both sequences.
Identifying the Common Terms:
- The first sequence has a common difference of 4, while the second sequence has a common difference of 7.
- We can write the general terms of the two sequences as follows:
- First sequence: a_1 = 3, a_n = 3 + 4(n-1)
- Second sequence: b_1 = 2, b_n = 2 + 7(n-1)
- To find the common terms, we need to equate the two expressions for the terms and solve for the value of n.
- 3 + 4(n-1) = 2 + 7(n-1)
- Simplifying the equation, we get: 4n - 1 = 7n - 5
- Rearranging the equation, we have: 3n = 4
- Solving for n, we find that n = 4/3.
- Since n is not a whole number, there are no common terms between the two sequences.
Conclusion:
- The number of terms common to the arithmetic progressions 3, 7, 11, ..., 407 and 2, 9, 16, ..., 709 is 0.
- Therefore, the correct answer is option 'A'.
Identifying the Common Terms:
- The first sequence has a common difference of 4, while the second sequence has a common difference of 7.
- We can write the general terms of the two sequences as follows:
- First sequence: a_1 = 3, a_n = 3 + 4(n-1)
- Second sequence: b_1 = 2, b_n = 2 + 7(n-1)
- To find the common terms, we need to equate the two expressions for the terms and solve for the value of n.
- 3 + 4(n-1) = 2 + 7(n-1)
- Simplifying the equation, we get: 4n - 1 = 7n - 5
- Rearranging the equation, we have: 3n = 4
- Solving for n, we find that n = 4/3.
- Since n is not a whole number, there are no common terms between the two sequences.
Conclusion:
- The number of terms common to the arithmetic progressions 3, 7, 11, ..., 407 and 2, 9, 16, ..., 709 is 0.
- Therefore, the correct answer is option 'A'.
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The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer?.
The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of terms common to the Arithmetic progressions 3, 7, 11, …., 407 and 2, 9, 16, …., 709 isa)14b)21c)51d)28Correct answer is option 'A'. Can you explain this answer?.
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