Pregunta
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3.4 Is -72 a term in the sequence? Justify your answer.
Which term in the sequence has a value of 8 ?

Ask by Goodwin Watson. in South Africa
Dec 16,2024

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The 31st term of the sequence is 8. -72 is not a term in the sequence.

Solución

To determine if -72 is a term in the given sequence, we first need to identify the pattern of the sequence. Let’s look at the differences between consecutive terms:
It appears that the difference between consecutive terms is consistently . This suggests that the sequence is an arithmetic sequence with a common difference of .
To find the term that equals 8, we can use the formula for the nth term of an arithmetic sequence:
where is the nth term, is the first term, is the term number, and is the common difference.
In this case, and . We want to find the value of such that :
Let’s solve for :
So, the 31st term of the sequence is 8.
Now, let’s check if -72 is a term in the sequence. We can use the same formula to find the term number for -72:
Solving for :
Since is a negative number, it is not possible for the sequence to have a negative term number. Therefore, -72 is not a term in the given sequence.

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Mind Expander

To determine if -72 is a term in the sequence given as , we need to analyze the pattern. The sequence appears to be an arithmetic sequence where each term is generated by adding a common difference. The common difference can be calculated as . Continuing this sequence, we can see that all terms remain negative, so -72 is not a term in the sequence.
To find which term in the sequence equals 8, we can set the nth term formula for an arithmetic sequence: . Here, and . Setting , we can solve for :
Simplifying this gives:
So, the 31st term in the sequence has a value of 8!

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