Problem 58
Question
Find the sum of the finite arithmetic sequence. $$1+4+7+10+13+16+19$$
Step-by-Step Solution
Verified Answer
The sum of the arithmetic sequence is 70.
1Step 1: Identify sequence type
The given sequence is an arithmetic sequence because there is a constant difference between consecutive terms.
2Step 2: 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 \(4 - 1 = 3.\)
3Step 3: 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.
4Step 4: 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 \( S = 7/2 * (1 + 19) = 70. \)
Other exercises in this chapter
Problem 57
Find the specified \(n\) th term in the expansion of the binomial. \((x-6 y)^{5}, n=3\)
View solution Problem 58
Write the first five terms of the sequence defined recursively. $$a_{0}=-1, a_{1}=5, a_{k}=a_{k-2}+a_{k-1}$$
View solution Problem 58
Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{10} C_{7}$$
View solution Problem 58
Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{6} 32\left(\frac{1}{4}\right)^{i-1}$$
View solution