Question

What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …

Answer 1

Answer:

A term at position n can be expressed as \[2*3^{n-1}\]

Step-by-step explanation:

The given geometric sequence is 2, 6, 18, 54, …

Starting term = 2

Second term = 6

So second term is 3 times the first term.

Similarly, Third term = 18

This is 3 times the second term, that is , 3 * 6

Fourth term is is 54.

This is 3 times the third term, that is , 3 * 18

Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]

where n represents the position of the term in the sequence.