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Chapter 7: Problem 26

Find the eighth term of an arithmetic sequence whose fourth term is 7 and whose fifth term is 4 .

Short Answer

Expert verified
The eighth term of the arithmetic sequence is \(-5\).

Step by step solution

01

Find the common difference

By the given information, we have the fourth term as 7 and the fifth term as 4. In an arithmetic progression, the common difference (d) is the same between consecutive terms. Therefore, we can find the common difference as follows: d = 5th term - 4th term d = 4 - 7 d = -3 So, the common difference is -3.
02

Find the first term

We can write the general formula for the nth term of an arithmetic sequence as: An = A1 + (n - 1)d Where An is the nth term, A1 is the first term, n is the term's position, and d is the common difference. We know the common difference is -3 and the fourth term (A4) is 7. Using the formula, we can find the first term (A1) as follows: 7 = A1 + (4 - 1)(-3) Simplifying the equation: 7 = A1 - 9 A1 = 7 + 9 A1 = 16 So, the first term of the arithmetic sequence is 16.
03

Find the eighth term

Now, we have the first term, A1 = 16, and the common difference, d = -3. We can plug these values into the formula to calculate the eighth term (A8): A8 = A1 + (8 - 1)d A8 = 16 + (7)(-3) A8 = 16 - 21 A8 = -5 Thus, the eighth term of this arithmetic sequence is -5.

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Most popular questions from this chapter

Find the sum of all the four-digit odd positive integers.

Define a sequence recursively by \(a_{1}=3 \quad\) and \(\quad a_{n+1}=\frac{1}{2}\left(\frac{7}{a_{n}}+a_{n}\right)\) for \(n \geq 1 .\) Find the smallest value of \(n\) such that \(a_{n}\) agrees with \(\sqrt{7}\) for at least six digits after the decimal point.

Find the ninth row of Pascal's triangle.

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