Question

6. Which table shows a geometric sequence? Term 1 23 4 5 Term 12 3 4 5 C Value 15 30 45 | 60 | 75 Value 918 27 36 45 Term 1 1 2 mo 4 5 Term 1 2 3 4 5 D Value 2 16 128 1024 8192 Value 220 260 300 340 380 7. Which Statement is TRUE? a. 1,-5, 25, -125, ... is a geometric sequence because to get to the next term, you multiply -5 times the previous term. b. 1, 8, 15, 22, 29, ... is a geometric sequence because to get to the next term, you multiply 8 times the previous term.

Answer 1

In a geomeric sequence each term is related to its previous by the product of a ratio. To find the ratio we need to divide each term by its previous and if the ratio is the same throughout the sequence, then it is a geometric sequence.

We need to check the ratio n the sequences.

A)

$\begin{gathered} \frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \frac{30}{15}=\frac{45}{30} \\ 2=1.5 \end{gathered}$

The equation isn't valid, therefore this is not a geometric sequence.

B)

$\begin{gathered} \frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \frac{16}{2}=\frac{128}{16} \\ 8=8 \end{gathered}$

The equation is valid, so the sequence is a geometric sequence. This is the correct answer.