In an arithmetic sequence, a_1=8 and a_4=20. What is its explicit rule?
Answer and explanation
Correct answer: a_n=4n+4
For an arithmetic sequence, the explicit rule is a_n=a_1+(n-1)d. From the first to the fourth term there are three equal gaps, so 3d=a_4-a_1=20-8=12, giving d=4. Substitute this into the formula: a_n=8+(n-1)4=8+4n-4=4n+4. Hence option B is correct. Option A gives a_1=12 rather than 8. Option C gives a_1=8 but a_4=23, so its difference is wrong. Option D gives a_1=8 but a_4=17. The key is dividing the total change by three gaps, not by four terms.
Frequently asked questions
What is the correct answer to this question?
a_n=4n+4
Why is this the correct answer?
For an arithmetic sequence, the explicit rule is a_n=a_1+(n-1)d. From the first to the fourth term there are three equal gaps, so 3d=a_4-a_1=20-8=12, giving d=4. Substitute this into the formula: a_n=8+(n-1)4=8+4n-4=4n+4. Hence option B is correct. Option A gives a_1=12 rather than 8. Option C gives a_1=8 but a_4=23, so its difference is wrong. Option D gives a_1=8 but a_4=17. The key is dividing the total change by three gaps, not by four terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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