If a_n = (-1)^n(n + 1), what will be the value of a_7 + a_8?
Answer and explanation
Correct answer: 1
The governing concept is evaluating an explicit sequence rule while tracking alternating signs. For n = 7, (-1)^7 = -1, so a_7 = -1(7 + 1) = -8. For n = 8, (-1)^8 = 1, so a_8 = 1(8 + 1) = 9. Therefore a_7 + a_8 = -8 + 9 = 1. Hence option B is correct. The sign changes because odd powers of -1 are negative and even powers are positive. Option A would reverse or mishandle one sign, while options C and D arise from adding the magnitudes incorrectly or ignoring the alternating factor. Substitution into the given rule is the safest method.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing concept is evaluating an explicit sequence rule while tracking alternating signs. For n = 7, (-1)^7 = -1, so a_7 = -1(7 + 1) = -8. For n = 8, (-1)^8 = 1, so a_8 = 1(8 + 1) = 9. Therefore a_7 + a_8 = -8 + 9 = 1. Hence option B is correct. The sign changes because odd powers of -1 are negative and even powers are positive. Option A would reverse or mishandle one sign, while options C and D arise from adding the magnitudes incorrectly or ignoring the alternating factor. Substitution into the given rule is the safest method.
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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