If \(a_n=(-1)^n(n+2)\), what is the value of \(a_6+a_7\)?
Answer and explanation
Correct answer: \(-1\)
Evaluate the explicit rule separately at the two required indices. For \(n=6\), \((-1)^6=1\), so \(a_6=1(6+2)=8\). For \(n=7\), \((-1)^7=-1\), so \(a_7=-1(7+2)=-9\). Therefore \(a_6+a_7=8+(-9)=-1\), and option A is correct. The key concept is the parity-dependent sign: even indices give a positive factor and odd indices give a negative factor. Options C and D incorrectly combine the magnitudes 8 and 9, while option B reverses the final sign.
Frequently asked questions
What is the correct answer to this question?
\(-1\)
Why is this the correct answer?
Evaluate the explicit rule separately at the two required indices. For \(n=6\), \((-1)^6=1\), so \(a_6=1(6+2)=8\). For \(n=7\), \((-1)^7=-1\), so \(a_7=-1(7+2)=-9\). Therefore \(a_6+a_7=8+(-9)=-1\), and option A is correct. The key concept is the parity-dependent sign: even indices give a positive factor and odd indices give a negative factor. Options C and D incorrectly combine the magnitudes 8 and 9, while option B reverses the final sign.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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