Question

quiz 14 (9.3, 9.4)
score: 2.2/6 answered: 3/6
question 4
find the sum: 7 + 9 + 11 + ... + 21
answer:
question help: message instructor

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence with first term \(a_1 = 7\), common difference \(d = 2\), and last term \(a_n=21\).

Step2: Find the number of terms \(n\)

Use the formula \(a_n=a_1+(n - 1)d\). Substitute \(a_n = 21\), \(a_1 = 7\), \(d = 2\):

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Step3: Calculate the sum \(S_n\)

Use the arithmetic series sum formula \(S_n=\frac{n(a_1 + a_n)}{2}\). Substitute \(n = 8\), \(a_1 = 7\), \(a_n = 21\):

$$ S_8=\frac{8\times(7 + 21)}{2}=\frac{8\times28}{2}=4\times28 = 112 $$

Answer:

\(112\)