If (a_n=(-1)^{n+1}n^2), what will be the value of (a_9+a_{10})?
Answer and explanation
Correct answer: -19
Given \(a_n=(-1)^{n+1}n^2\), \(a_9=(-1)^{10}\times9^2=81\) and \(a_{10}=(-1)^{11}\times10^2=-100\). Hence, \(a_9+a_{10}=81-100=-19\). The option \(-181\) may result from adding both magnitudes and then assigning a negative sign, which is incorrect. Exam tip: check the sign of \((-1)^{n+1}\) separately for odd and even values of \(n\).
Frequently asked questions
What is the correct answer to this question?
-19
Why is this the correct answer?
Given \(a_n=(-1)^{n+1}n^2\), \(a_9=(-1)^{10}\times9^2=81\) and \(a_{10}=(-1)^{11}\times10^2=-100\). Hence, \(a_9+a_{10}=81-100=-19\). The option \(-181\) may result from adding both magnitudes and then assigning a negative sign, which is incorrect. Exam tip: check the sign of \((-1)^{n+1}\) separately for odd and even values of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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