If aₙ = 9n + 2, which term is equal to 146?
Answer and explanation
Correct answer: n = 16
The governing concept is using an explicit term rule in reverse to find the position of a specified value. Set the general expression equal to 146: 9n + 2 = 146. Subtract 2 from both sides to obtain 9n = 144, and divide by 9 to get n = 16. Hence the value 146 is the 16th term, so option C is correct. Verification gives a₁₆ = 9(16) + 2 = 144 + 2 = 146. Option B gives 137, while option D gives 155; option A gives 128. The essential step is solving the equation for the term number rather than substituting a guessed position into the sequence.
Frequently asked questions
What is the correct answer to this question?
n = 16
Why is this the correct answer?
The governing concept is using an explicit term rule in reverse to find the position of a specified value. Set the general expression equal to 146: 9n + 2 = 146. Subtract 2 from both sides to obtain 9n = 144, and divide by 9 to get n = 16. Hence the value 146 is the 16th term, so option C is correct. Verification gives a₁₆ = 9(16) + 2 = 144 + 2 = 146. Option B gives 137, while option D gives 155; option A gives 128. The essential step is solving the equation for the term number rather than substituting a guessed position into the sequence.
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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