If the first term of a geometric progression is 18 and the common ratio is \(\frac{1}{3}\), what is the second term?

6

The governing concept is the term-to-term rule of a geometric progression: every term is obtained by multiplying the preceding term by the same common ratio. Here the first term is 18 and the ratio is \(\frac{1}{3}\). Therefore, the second term is \(a_2=a_1r=18\times\frac{1}{3}=6\). Option B is correct. The value 3 would result from an incorrect division by 6, while 9 and 12 do not follow from multiplying 18 by one-third. Since the ratio is less than 1, the next term is smaller than the first term.

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.