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Chapter 9: Problem 57

Find the sum of the finite arithmetic sequence. $$2+4+6+8+10+12+14+16+18+20$$

Short Answer

Expert verified
The sum of the arithmetic sequence is 110.

Step by step solution

01

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.
02

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: \(S = \frac{10}{2} (2 + 20)\)
03

Calculate the sum

Calculate the sum \(S\) as per the substituted formula: \(S = 5 * 22 = 110\)

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