In the sequence \((81,27,9,3,\ldots)\), each term is \(\frac{1}{3}\) of the previous term. What is the sixth term?
Answer and explanation
Correct answer: \(\frac{1}{3}\)
The governing concept is a geometric sequence, because every term is obtained by multiplying the preceding term by the constant ratio \(r=\frac13\). Starting with 81, the terms are \(81,27,9,3,1,\frac13\). Equivalently, the sixth term is \(a_6=81\left(\frac13\right)^5=\frac{81}{243}=\frac13\). Hence option B is correct. Option A is the fifth term, not the sixth; option C would result from applying the ratio one extra time, and option D is impossible because repeated division by 3 never makes this positive sequence exactly zero.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{3}\)
Why is this the correct answer?
The governing concept is a geometric sequence, because every term is obtained by multiplying the preceding term by the constant ratio \(r=\frac13\). Starting with 81, the terms are \(81,27,9,3,1,\frac13\). Equivalently, the sixth term is \(a_6=81\left(\frac13\right)^5=\frac{81}{243}=\frac13\). Hence option B is correct. Option A is the fifth term, not the sixth; option C would result from applying the ratio one extra time, and option D is impossible because repeated division by 3 never makes this positive sequence exactly zero.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
