If (a_n=(-1)^{n+1}(3n-2)), what is the value of (a_5)?
Answer and explanation
Correct answer: (13)
Substitute n=5 directly into the given formula. The sign factor becomes \((-1)^{5+1}=(-1)^6=1\), because an even power of -1 equals 1. The numerical factor is \(3(5)-2=15-2=13\). Multiplying these parts gives \(a_5=1\times13=13\).
Therefore option A is correct. The most important point is to evaluate both parts of the product and to check the parity of the exponent before assigning the sign. If the exponent had been odd, the sign would have been negative, but here it is even. The value \(-13\) would result from missing this sign check, while 17 and -17 come from an arithmetic error in \(3n-2\). The supplied answer and explanation are correct.
Frequently asked questions
What is the correct answer to this question?
(13)
Why is this the correct answer?
Substitute n=5 directly into the given formula. The sign factor becomes \((-1)^{5+1}=(-1)^6=1\), because an even power of -1 equals 1. The numerical factor is \(3(5)-2=15-2=13\). Multiplying these parts gives \(a_5=1\times13=13\).
Therefore option A is correct. The most important point is to evaluate both parts of the product and to check the parity of the exponent before assigning the sign. If the exponent had been odd, the sign would have been negative, but here it is even. The value \(-13\) would result from missing this sign check, while 17 and -17 come from an arithmetic error in \(3n-2\). The supplied answer and explanation are correct.
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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