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: aₙ = a + (n − 1)d. Here the first term is a = 13, and the common difference is d = 19 − 13 = 6. For the fourteenth term, substitute n = 14: a₁₄ = 13 + (14 − 1) × 6 = 13 + 13 × 6 = 13 + 78 = 91. Therefore, option B is correct. Option A results from adding only twelve differences, while option C adds one difference too many; option D uses an incorrect difference or term count. The answer can also be checked by continuing the sequence: each successive term increases by 6, and the fourteenth term is 91.
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: aₙ = a + (n − 1)d. Here the first term is a = 13, and the common difference is d = 19 − 13 = 6. For the fourteenth term, substitute n = 14: a₁₄ = 13 + (14 − 1) × 6 = 13 + 13 × 6 = 13 + 78 = 91. Therefore, option B is correct. Option A results from adding only twelve differences, while option C adds one difference too many; option D uses an incorrect difference or term count. The answer can also be checked by continuing the sequence: each successive term increases by 6, and the fourteenth term is 91.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
