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consider the following first four terms of a sequence.
54, 41, 28, 15, ...
determine whether the given sequence is geometric, arithmetic, or neither.
the given sequence is:
geometric
neither geometric nor arithmetic
arithmetic
determine the fifth and sixth terms of the sequence.
$a_5 = \square$
$a_6 = \square$

Explanation:

Step1: Check arithmetic sequence

Calculate differences between terms:
$41 - 54 = -13$
$28 - 41 = -13$
$15 - 28 = -13$
The common difference $d=-13$ is constant.

Step2: Check geometric sequence

Calculate ratios between terms:
$\frac{41}{54} \approx 0.759$
$\frac{28}{41} \approx 0.683$
The ratios are not equal, so it is not geometric.

Step3: Find fifth term $a_5$

Use arithmetic sequence formula $a_n = a_1 + (n-1)d$
$a_5 = 54 + (5-1)(-13) = 54 - 52 = 2$

Step4: Find sixth term $a_6$

$a_6 = 54 + (6-1)(-13) = 54 - 65 = -11$

Answer:

The given sequence is: Arithmetic
$a_5 = 2$
$a_6 = -11$