Questions: Help Acellus Learning Unit Exam - Reasoning and Proofs Find the next two terms in this sequence. 1,3,9,27,81,[ ? ],[ ]

Solution Steps

The sequence given is a geometric sequence where each term is multiplied by a constant factor to get the next term. To find the next two terms, identify the common ratio by dividing the second term by the first term, and then multiply the last known term by this common ratio to find the subsequent terms.

The given sequence is \( 1, 3, 9, 27, 81 \). This sequence can be recognized as a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio.

To find the common ratio \( r \), we can calculate: \[ r = \frac{3}{1} = 3 \] This ratio holds for the subsequent terms as well: \[ \frac{9}{3} = 3, \quad \frac{27}{9} = 3, \quad \frac{81}{27} = 3 \]

Using the common ratio \( r = 3 \), we can find the next two terms in the sequence:

• The next term after \( 81 \) is: \[ 81 \times 3 = 243 \]
• The term following \( 243 \) is: \[ 243 \times 3 = 729 \]

Final Answer