If (a_n=11n-6), what is (a_7-a_2)?
Answer and explanation
Correct answer: (55)
Use the given general rule \(a_n=11n-6\) separately for the two required positions. For \(n=7\), \(a_7=11(7)-6=77-6=71\). For \(n=2\), \(a_2=11(2)-6=22-6=16\). The requested expression is \(a_7-a_2\), so its value is \(71-16=55\). This also agrees with the fact that moving from the second to the seventh position covers five steps of size 11.
The answer must be the difference, not the value of \(a_7\) alone or the value of \(a_2\) alone. Careful substitution and subtraction lead to 55. Since 55 appears in option B, option B is correct. The other numerical choices do not result from the stated rule and the requested subtraction.
Frequently asked questions
What is the correct answer to this question?
(55)
Why is this the correct answer?
Use the given general rule \(a_n=11n-6\) separately for the two required positions. For \(n=7\), \(a_7=11(7)-6=77-6=71\). For \(n=2\), \(a_2=11(2)-6=22-6=16\). The requested expression is \(a_7-a_2\), so its value is \(71-16=55\). This also agrees with the fact that moving from the second to the seventh position covers five steps of size 11.
The answer must be the difference, not the value of \(a_7\) alone or the value of \(a_2\) alone. Careful substitution and subtraction lead to 55. Since 55 appears in option B, option B is correct. The other numerical choices do not result from the stated rule and the requested subtraction.
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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