Question

Evaluate each sequence's related arithmetic series. 1, 2 and 3 please.

Answer 1

In order to evaluate the sequences, let's find the ratio of each one by subtracting the second term and the first one.

1)

`\begin{gathered} 1,-5,-11,\ldots \\ r=-5-1=-6 \end{gathered}`

Since the ratio is negative, the sequence is decrescent.

2)

`\begin{gathered} 2.5,5.5,8.5,\ldots \\ r=5.5-2.5=3 \end{gathered}`

The ratio is positive, so we have a crescent sequence.

3)

`\begin{gathered} 4.7,8.7,12.7,\ldots \\ r=8.7-4.7=4 \end{gathered}`

The ratio is positive, so we have a crescent sequence.