If a_n=\frac{2n+3}{n+1}, what is a_4?
Answer and explanation
Correct answer: \frac{11}{5}
The governing skill is evaluating an explicit fractional rule at a specified index. To find a_4, replace every n in both the numerator and denominator by 4: a_4=(2(4)+3)/(4+1)=(8+3)/5=11/5. Therefore option C is correct. A common error is to substitute 4 only in the numerator, only in the denominator, or to add the numerator and denominator instead of forming their quotient. Option A would correspond to an incorrect numerator, option B simplifies to 2 and does not equal the calculated fraction, and option D uses 12 rather than 11 in the numerator. Keeping the fraction unsimplified also makes the substitution transparent.
Frequently asked questions
What is the correct answer to this question?
\frac{11}{5}
Why is this the correct answer?
The governing skill is evaluating an explicit fractional rule at a specified index. To find a_4, replace every n in both the numerator and denominator by 4: a_4=(2(4)+3)/(4+1)=(8+3)/5=11/5. Therefore option C is correct. A common error is to substitute 4 only in the numerator, only in the denominator, or to add the numerator and denominator instead of forming their quotient. Option A would correspond to an incorrect numerator, option B simplifies to 2 and does not equal the calculated fraction, and option D uses 12 rather than 11 in the numerator. Keeping the fraction unsimplified also makes the substitution transparent.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
