What is the fourteenth term of the arithmetic progression (13, 19, 25, 31, …)?
Answer and explanation
Correct answer: 91
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n - 1)d. The first term is a = 13, and the common difference is d = 19 - 13 = 6. For the fourteenth term, use n = 14: a_14 = 13 + (14 - 1)6 = 13 + 78 = 91. Hence option B is correct. The number of intervals from the first term to the fourteenth term is 13, which explains the factor (14 - 1). Option A results from using only 12 intervals, and option C results from using 14 intervals instead of 13. Option D uses an incorrect difference or index. Substitution into the standard formula gives an exact and unambiguous result.
Frequently asked questions
What is the correct answer to this question?
91
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n - 1)d. The first term is a = 13, and the common difference is d = 19 - 13 = 6. For the fourteenth term, use n = 14: a_14 = 13 + (14 - 1)6 = 13 + 78 = 91. Hence option B is correct. The number of intervals from the first term to the fourteenth term is 13, which explains the factor (14 - 1). Option A results from using only 12 intervals, and option C results from using 14 intervals instead of 13. Option D uses an incorrect difference or index. Substitution into the standard formula gives an exact and unambiguous result.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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