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Chapter 14: Problem 100

Will help you prepare for the material covered in the next section. Use the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence \(4,-3,-10, \ldots\)

Short Answer

Expert verified
The eighth term of the arithmetic sequence is \(a_{8}= -45\).

Step by step solution

01

Recognize the Type of Sequence

Recognize that the sequence \(4,-3,-10, \ldots\) is an arithmetic sequence. In an arithmetic sequence, each term is determined by adding a fixed number to the previous term. Here, the fixed number is -7. This is confirmed by the given formula \(a_{n}=4+(n-1)(-7)\), which represents the nth term of an arithmetic sequence.
02

Apply the Given Formula

Apply the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence. Replace n in the formula with 8. So, \(a_{8} = 4+(8-1)(-7)\).
03

Evaluate the Expression

Calculate the expression \(4+(8-1)(-7)\) to find the value of the eighth term in the sequence. The sequence is decreasing by 7 each time, so after 7 steps past the first term, it will have decreased by \(7 \times -7 = -49\). Add this to the starting number (4) to get the eighth term, so \(a_{8} = 4 + -49\).
04

Final Calculation

Add 4 and -49 to find the eighth term. So, \(a_{8} = -45\).

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