Chapter 11: Q11. (page 586)

Find the sum of each arithmetic series.
$\sum_{k = 3}^{7} (3 k + 4)$

Short Answer

Expert verified

The sum of the arithmetic series is95.

Step by step solution

Step 1. Given Information.

Given arithmetic series is $\sum_{k = 3}^{7} (3 k + 4)$ .

Step 2. Calculation.

From the summation, the number of terms is $n = 5$

The first term is given by plugging $k = 3$ :

$\begin{array}{l} a_{k} = 3 k + 4 \\ a_{3} = 3 (3) + 4 \\ a_{3} = 9 + 4 \\ a_{3} = 13 \end{array}$

The last term is given by plugging $k = 7$ :

$\begin{array}{l} a_{k} = 3 k + 4 \\ a_{7} = 3 (7) + 4 \\ a_{7} = 21 + 4 \\ a_{7} = 25 \end{array}$

The sum $S_{n}$ of the first n terms of an arithmetic series is given by

$S_{n} = \frac{n}{2} (a_{1} + a_{n})$

Here, $a_{1} = 13, n = 5, a_{n} = 25$

Plugging the values:

$\begin{array}{l} S_{n} = \frac{n}{2} (a_{1} + a_{n}) \\ S_{5} = \frac{5}{2} (13 + 25) \\ S_{5} = \frac{5}{2} (38) \\ S_{5} = 5 (19) \\ S_{5} = 95 \end{array}$

Step 3. Conclusion.

Hence, the sum is 95.

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Find the sum of each arithmetic series.
$\sum_{k = 3}^{7} (3 k + 4)$

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Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Find the sum of each arithmetic series.∑k=37(3k+4)

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Step by step solution

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Step 3. Conclusion.

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Find the sum of each arithmetic series.
$\sum_{k = 3}^{7} (3 k + 4)$