If a_n = pn + 7 and a_8 = 71, what is the value of p?
Answer and explanation
Correct answer: 8
The governing concept is substitution into an explicit sequence rule. The notation a_8 means that n must be replaced by 8 in a_n = pn + 7. Thus, 8p + 7 = 71. Subtracting 7 from both sides gives 8p = 64, and dividing by 8 gives p = 8. A quick check confirms the result: a_8 = 8(8) + 7 = 64 + 7 = 71. Option A would give 55, option B would give 63, and option D would give 79, so none of them satisfies the given eighth term. Therefore, option C is the only correct answer. The important point is to use the index 8, not the first term or the coefficient itself, when applying the rule.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The governing concept is substitution into an explicit sequence rule. The notation a_8 means that n must be replaced by 8 in a_n = pn + 7. Thus, 8p + 7 = 71. Subtracting 7 from both sides gives 8p = 64, and dividing by 8 gives p = 8. A quick check confirms the result: a_8 = 8(8) + 7 = 64 + 7 = 71. Option A would give 55, option B would give 63, and option D would give 79, so none of them satisfies the given eighth term. Therefore, option C is the only correct answer. The important point is to use the index 8, not the first term or the coefficient itself, when applying the rule.
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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