If (a_n=15-2n), when will (a_n) be zero?
Answer and explanation
Correct answer: No integral term
To find when a term is zero, set the explicit rule equal to zero: aₙ = 15 − 2n = 0. Solving gives 2n = 15 and n = 15/2 = 7.5. Sequence indices are positive integers, so there is no integral term number equal to 7.5. Consequently, no term of this sequence is exactly zero, and option A is correct. Checking nearby valid indices confirms this: a₇ = 15 − 14 = 1 and a₈ = 15 − 16 = −1, so the sequence passes from positive to negative without taking zero at an integer index. Options B and C identify neighbouring terms but neither is zero, while D is unrelated.
Frequently asked questions
What is the correct answer to this question?
No integral term
Why is this the correct answer?
To find when a term is zero, set the explicit rule equal to zero: aₙ = 15 − 2n = 0. Solving gives 2n = 15 and n = 15/2 = 7.5. Sequence indices are positive integers, so there is no integral term number equal to 7.5. Consequently, no term of this sequence is exactly zero, and option A is correct. Checking nearby valid indices confirms this: a₇ = 15 − 14 = 1 and a₈ = 15 − 16 = −1, so the sequence passes from positive to negative without taking zero at an integer index. Options B and C identify neighbouring terms but neither is zero, while D is unrelated.
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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