In a sequence, (a_n=7n-5). What is (a_{n+1}-a_n)?
Answer and explanation
Correct answer: (7)
The sequence rule is linear: each term is obtained by multiplying its position by 7 and then subtracting 5. To find the change from one term to the next, first replace n by n+1. This gives \(a_{n+1}=7(n+1)-5=7n+2\). Now subtract the original term: \(a_{n+1}-a_n=(7n+2)-(7n-5)=7\). The variable terms cancel completely.
Therefore, option A, 7, is correct. The result can also be understood without expansion: increasing n by 1 increases \(7n\) by 7, while the constant \(-5\) does not change. Options 5 and 2 confuse the constant or the new expression with the difference. The supplied answer and explanation correctly identify the constant first difference of this linear sequence.
Frequently asked questions
What is the correct answer to this question?
(7)
Why is this the correct answer?
The sequence rule is linear: each term is obtained by multiplying its position by 7 and then subtracting 5. To find the change from one term to the next, first replace n by n+1. This gives \(a_{n+1}=7(n+1)-5=7n+2\). Now subtract the original term: \(a_{n+1}-a_n=(7n+2)-(7n-5)=7\). The variable terms cancel completely.
Therefore, option A, 7, is correct. The result can also be understood without expansion: increasing n by 1 increases \(7n\) by 7, while the constant \(-5\) does not change. Options 5 and 2 confuse the constant or the new expression with the difference. The supplied answer and explanation correctly identify the constant first difference of this linear sequence.
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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