Problem 57
Question
Find the sum of the finite arithmetic sequence. $$2+4+6+8+10+12+14+16+18+20$$
Step-by-Step Solution
Verified Answer
The sum of the arithmetic sequence is 110.
1Step 1: Identify the first term, last term, and number of terms
Observe the sequence: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. It can be seen that the first term \(a_l\) is 2, the last term \(a_n\) is 20, and the number of terms \(n\) is 10.
2Step 2: Apply the formula for the sum of an arithmetic sequence
The formula for the sum of an arithmetic sequence is: \(S = \frac{n}{2} (a_l + a_n)\). Substituting the identified values from Step 1 into the formula gives: \(S = \frac{10}{2} (2 + 20)\)
3Step 3: Calculate the sum
Calculate the sum \(S\) as per the substituted formula: \(S = 5 * 22 = 110\)
Other exercises in this chapter
Problem 56
Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=1}^{9}(-2)^{n-1}$$
View solution Problem 57
Write the first five terms of the sequence defined recursively. $$a_{0}=1, a_{1}=3, a_{k}=a_{k-2}+a_{k-1}$$
View solution Problem 57
Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{i=1}^{2} 64\left(-\frac{1}{2}\right)^{i-1}$$
View solution Problem 57
Find the specified \(n\) th term in the expansion of the binomial. \((x-6 y)^{5}, n=3\)
View solution