Class 10 Exam > Class 10 Questions > The 15th term from the last term of the AP: 4...
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The 15th term from the last term of the AP: 4,9,14,......254 is :
- a)100
- b)184
- c)284
- d)174
Correct answer is option 'B'. Can you explain this answer?
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The 15th term from the last term of the AP: 4,9,14,......254 is :a)100...
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The 15th term from the last term of the AP: 4,9,14,......254 is :a)100...
Understanding the AP Sequence
The given arithmetic progression (AP) is: 4, 9, 14, ..., 254.
Identifying the First Term and Common Difference
- First Term (a): The first term (a) is 4.
- Common Difference (d): The difference between consecutive terms is 5 (9 - 4 = 5).
Finding the Total Number of Terms
To find the total number of terms (n) in the AP, we use the formula for the nth term of an AP:
- nth term formula: a_n = a + (n - 1) * d
Setting a_n to 254, we solve for n:
- 254 = 4 + (n - 1) * 5
- 250 = (n - 1) * 5
- n - 1 = 50
- n = 51
Thus, there are 51 terms in this AP.
Finding the 15th Term from the Last
To find the 15th term from the last (51st term), we calculate the (51 - 15 + 1) = 37th term:
- 37th term formula: a_37 = a + (37 - 1) * d
- a_37 = 4 + (36 * 5)
- a_37 = 4 + 180
- a_37 = 184
Conclusion
The 15th term from the last term of the AP is 184. Thus, the correct answer is option 'B'.
The given arithmetic progression (AP) is: 4, 9, 14, ..., 254.
Identifying the First Term and Common Difference
- First Term (a): The first term (a) is 4.
- Common Difference (d): The difference between consecutive terms is 5 (9 - 4 = 5).
Finding the Total Number of Terms
To find the total number of terms (n) in the AP, we use the formula for the nth term of an AP:
- nth term formula: a_n = a + (n - 1) * d
Setting a_n to 254, we solve for n:
- 254 = 4 + (n - 1) * 5
- 250 = (n - 1) * 5
- n - 1 = 50
- n = 51
Thus, there are 51 terms in this AP.
Finding the 15th Term from the Last
To find the 15th term from the last (51st term), we calculate the (51 - 15 + 1) = 37th term:
- 37th term formula: a_37 = a + (37 - 1) * d
- a_37 = 4 + (36 * 5)
- a_37 = 4 + 180
- a_37 = 184
Conclusion
The 15th term from the last term of the AP is 184. Thus, the correct answer is option 'B'.
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The 15th term from the last term of the AP: 4,9,14,......254 is :a)100b)184c)284d)174Correct answer is option 'B'. 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 15th term from the last term of the AP: 4,9,14,......254 is :a)100b)184c)284d)174Correct answer is option 'B'. 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 15th term from the last term of the AP: 4,9,14,......254 is :a)100b)184c)284d)174Correct answer is option 'B'. Can you explain this answer?.
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