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Chapter 15: Problem 47

Find the sum of the first 10 terms of the arithmetic sequence with first term 14 and last term 68 .

Short Answer

Expert verified
The sum of the first 10 terms of the given arithmetic sequence is 410.

Step by step solution

01

Identify the given values

We are given the following: - First term (\(a_1\)) = 14 - Last term (\(a_{10}\)) = 68 - Number of terms (n) = 10
02

Use the arithmetic series formula

Using the arithmetic series formula, we can find the sum of the first 10 terms (\(S_{10}\)): \(S_{10} = \frac{n(a_1 + a_{10})}{2}\) Plugging in the given values:
03

Plug the given values into the formula

\(S_{10} = \frac{10(14 + 68)}{2}\)
04

Simplify and solve for the sum of the first 10 terms

Now, we can simplify the expression and find the sum: \(S_{10} = \frac{10(82)}{2}\) \(S_{10} = \frac{820}{2}\) \(S_{10} = 410\)
05

State the answer

The sum of the first 10 terms of the given arithmetic sequence is 410.

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