Chapter 12: Q 12.39. (page 1183)

Find the sum: $\sum_{i = 1}^{30} (6 i - 4)$

Short Answer

Expert verified

The obtained sum is 2670.

Step by step solution

Step 1. Given Information.

Consider the given sum: $\sum_{i = 1}^{30} (6 i - 4)$

simplify the sum.

Express the sum and identify the values.

$\begin{array}{rcl} \sum_{i = 1}^{30} (6 i - 4) & = & (6 (1) - 4) + (6 (2) - 4) + (6 (3) - 4) + \dots + (6 (30) - 4) \\ = & 2 + 8 + 14 + \dots + 176 \\ = & a_{1} + a_{2} + a_{3} + \dots + a_{30} \end{array}$

Thus, the obtained values are $a_{1} = 2$ and $a_{30} = 176$ .

Step 3. Find the sum.

Substitute the values in the some formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$

$\begin{array}{rcl} S_{30} & = & \frac{30}{2} (2 + 176) \\ = & 15 (178) \\ = & 2670 \end{array}$

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Find the sum: $\sum_{i = 1}^{30} (6 i - 4)$

Short Answer

Step by step solution

Step 1. Given Information.

simplify the sum.

Step 3. Find the sum.

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Find the sum: $\sum_{i = 1}^{30} (6 i - 4)$