If (a_n=4n+(-1)^{n+1}), what will be the value of (a_8)?
Answer and explanation
Correct answer: 31
Given \(a_n=4n+(-1)^{n+1}\). Substituting \(n=8\), \(a_8=4\times 8+(-1)^{8+1}=32+(-1)^9=32-1=31\). Hence, 31 is correct. The value 33 would result from incorrectly taking \((-1)^9\) as \(+1\); an odd power of \(-1\) is \(-1\). Exam tip: an even power of \(-1\) is \(+1\), while an odd power is \(-1\).
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
Given \(a_n=4n+(-1)^{n+1}\). Substituting \(n=8\), \(a_8=4\times 8+(-1)^{8+1}=32+(-1)^9=32-1=31\). Hence, 31 is correct. The value 33 would result from incorrectly taking \((-1)^9\) as \(+1\); an odd power of \(-1\) is \(-1\). Exam tip: an even power of \(-1\) is \(+1\), while an odd power is \(-1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
