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Chapter 9: Problem 58

Find the sum of the finite arithmetic sequence. $$1+4+7+10+13+16+19$$

Short Answer

Expert verified
The sum of the arithmetic sequence is 70.

Step by step solution

01

Identify sequence type

The given sequence is an arithmetic sequence because there is a constant difference between consecutive terms.
02

Find the common difference

The common difference of the arithmetic sequence can be found by subtracting the first term from the second term. In this case, it's \(4 - 1 = 3.\)
03

Find the number of terms

To find the number of terms, take the last term in the sequence, subtract the first term, divide by the common difference, and add 1. This yields \( (19 -1) / 3 + 1 = 7.\) There are 7 terms in the sequence.
04

Sum of arithmetic sequence

The sum \( S \) of an arithmetic sequence can be calculated using the formula \( S = n/2 * (a + l) \) where \( n \) is the number of terms, \( a \) is the first term and \( l \) is the last term. Substituting the given values, we get \( S = 7/2 * (1 + 19) = 70. \)

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Most popular questions from this chapter

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$3,7,11,15,19, \ldots$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(y^{2}+2\right)^{6}\)

Use the Binomial Theorem to expand and simplify the expression.\((y-5)^{4}\)

Explain how to use the first two terms of an arithmetic sequence to find the \(n\) th term.

Use a graphing utility to find the partial sum. $$\sum_{n=1}^{20}(2 n+1)$$
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