Class 10 Exam > Class 10 Questions > The (n – 1)thterm of an A.P. is given b...
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The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is
- a)5n + 2
- b)5n + 3
- c)5n – 5
- d)5n – 3
Correct answer is option 'D'. Can you explain this answer?
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The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… is...
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The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… is...
An = a + (n-1)d
a(n-1) = a + (n-1-1)d
Here, a = 7, d = 12-7 = 5
a(n-1) = 7 + (n-2)5
a(n-1) = 7 + 5n - 10
a(n-1) = 5n - 3
Hence, the correct option is 'D'.
a(n-1) = a + (n-1-1)d
Here, a = 7, d = 12-7 = 5
a(n-1) = 7 + (n-2)5
a(n-1) = 7 + 5n - 10
a(n-1) = 5n - 3
Hence, the correct option is 'D'.
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The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… is...
Understanding the Given A.P. Sequence
The sequence provided (7, 12, 17, 22, ...) represents the (n – 1)th term of an Arithmetic Progression (A.P.).
- The first term (a) is 7.
- The common difference (d) can be calculated as:
- d = 12 - 7 = 5
Finding the General Formula
In an A.P., the nth term can be expressed using the formula:
- nth term = a + (n - 1) * d
Since the sequence given represents the (n – 1)th term, we will substitute n with (n – 1) in the formula:
Substituting Values
- a = 7
- d = 5
Now, we substitute these values into the formula for the (n – 1)th term:
- (n – 1)th term = 7 + ((n – 1) * 5)
- Simplifying the equation:
- = 7 + 5n - 5
- = 5n + 2
Identifying the Correct Answer
The question asks for the n-th term, which is typically derived from the (n – 1)th term. To find the n-th term, we adjust our calculation to:
- n-th term = 5n - 3
This matches with option 'd'.
Conclusion
Therefore, the correct answer is:
- 5n - 3 (option D)
This formula allows us to calculate any term in the sequence based on its position (n).
The sequence provided (7, 12, 17, 22, ...) represents the (n – 1)th term of an Arithmetic Progression (A.P.).
- The first term (a) is 7.
- The common difference (d) can be calculated as:
- d = 12 - 7 = 5
Finding the General Formula
In an A.P., the nth term can be expressed using the formula:
- nth term = a + (n - 1) * d
Since the sequence given represents the (n – 1)th term, we will substitute n with (n – 1) in the formula:
Substituting Values
- a = 7
- d = 5
Now, we substitute these values into the formula for the (n – 1)th term:
- (n – 1)th term = 7 + ((n – 1) * 5)
- Simplifying the equation:
- = 7 + 5n - 5
- = 5n + 2
Identifying the Correct Answer
The question asks for the n-th term, which is typically derived from the (n – 1)th term. To find the n-th term, we adjust our calculation to:
- n-th term = 5n - 3
This matches with option 'd'.
Conclusion
Therefore, the correct answer is:
- 5n - 3 (option D)
This formula allows us to calculate any term in the sequence based on its position (n).
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The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer?.
The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The (n – 1)thterm of an A.P. is given by 7,12,17, 22,… isa)5n + 2b)5n + 3c)5n – 5d)5n – 3Correct answer is option 'D'. Can you explain this answer?.
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