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Chapter 5: Problem 35

Find the indicated term for the arithmetic sequence with first term, \(a_{1}\), and common difference, \(d\). Find \(a_{90}\), when \(a_{1}=-70, d=-2\).

Short Answer

Expert verified
The 90th term of the given arithmetic sequence, \(a_{90}\), is -248.

Step by step solution

01

Understanding Arithmetic Sequence

In an arithmetic sequence, each term after the first is obtained by adding a constant difference to the previous term. The formula to find the nth term in an arithmetic sequence is \(a_{n} = a_{1} + (n-1)*d\), where \(a_{n}\) is the nth term, \(a_{1}\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
02

Implementing the Formula

Given \(a_{1} = -70\), \(d = -2\), and we need to find \(a_{90}\). By substituting the values into the formula, we get \(a_{90} = -70 + (90-1)*(-2)\).
03

Calculating \(a_{90}\)

Calculate the value by solving the expression: \(a_{90} = -70 + 89*(-2)\). Which is \(a_{90} = -70 - 178\), hence \(a_{90} = -248\)

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Most popular questions from this chapter

For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: The number of students with the flu is increasing arithmetically or is increasing geometrically? Explain your answer.

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=0.1\)

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