What is the general term of the arithmetic progression (4,11,18,25,\ldots)?
Answer and explanation
Correct answer: (a_n=7n-3)
The governing concept is the explicit or general term of an arithmetic progression, a_n = a + (n − 1)d. The first term is a = 4, and the common difference is d = 11 − 4 = 7. Substitution gives a_n = 4 + (n − 1)7 = 4 + 7n − 7 = 7n − 3. Therefore option A is correct. A quick check is useful: for n = 1, option A gives 7(1) − 3 = 4, and for n = 2 it gives 14 − 3 = 11, matching the sequence. Option B gives 11 for the first term, option C gives 11, and option D gives 10; hence they fail the initial-term test even before later terms are considered.
Frequently asked questions
What is the correct answer to this question?
(a_n=7n-3)
Why is this the correct answer?
The governing concept is the explicit or general term of an arithmetic progression, a_n = a + (n − 1)d. The first term is a = 4, and the common difference is d = 11 − 4 = 7. Substitution gives a_n = 4 + (n − 1)7 = 4 + 7n − 7 = 7n − 3. Therefore option A is correct. A quick check is useful: for n = 1, option A gives 7(1) − 3 = 4, and for n = 2 it gives 14 − 3 = 11, matching the sequence. Option B gives 11 for the first term, option C gives 11, and option D gives 10; hence they fail the initial-term test even before later terms are considered.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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