Answer:
The characteristic of an arithmetic sequence is:
- <em>The</em><em> </em><em>difference</em><em> </em><em>between</em><em> </em><em>the</em><em> </em><em>consecutive</em><em> </em><em>terms</em><em> </em><em>is</em><em> </em><em>constant</em><em>.</em><em> </em>
This difference between consecutive terms is called <u>common</u><u> </u><u>difference</u> and is denoted by (d)
<h3>STEP I</h3>
(finding the common difference)
As stated above, the common difference is the difference between consecutive terms and, thus, will be found out by subtracting any two consecutive terms.
-7 and -23 are two consecutive terms in the sequence!
<u>Subtracting</u><u> </u><u>(</u><u>-</u><u>7</u><u>)</u><u> </u><u>from</u><u> </u><u>(</u><u>-</u><u>2</u><u>3</u><u>)</u><u>:</u>
<h3>STEP II</h3>
(Finding the nth term)
The formula used for finding the nth term of an arithmetic sequence is:
Here,
- = nth term
- a = first term
- d = common difference
The question asks us to find the 54th term of the sequence.
<em>Substituting 54 for </em>n:
- The first term of the sequence is -7
<em>substituting </em><em>-</em><em>7</em><em> </em><em>for</em><em> </em><em>a</em><em> </em><em>and</em><em> </em><em>-</em><em>1</em><em>6</em><em> </em><em>f</em><em>or</em><em> </em><em>d</em>
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<h3>ANSWER<em>:</em></h3>
The 54th term of the sequence is <u>-</u><u>8</u><u>5</u><u>5</u>.
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Learn more about nth term of an AP here:
brainly.com/question/16613594
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Hope this helps!