Precalculus Examples

$\sum_{n = 1}^{4} 5 n - 3$

Step 1

Expand the series for each value of $n$ .

$5 \cdot 1 - 3 + 5 \cdot 2 - 3 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2

Simplify.

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Step 2.1

Multiply $5$ by $1$ .

$5 - 3 + 5 \cdot 2 - 3 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2.2

Subtract $3$ from $5$ .

$2 + 5 \cdot 2 - 3 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2.3

Multiply $5$ by $2$ .

$2 + 10 - 3 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2.4

Subtract $3$ from $10$ .

$2 + 7 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2.5

Add $2$ and $7$ .

$9 + 5 \cdot 3 - 3 + 5 \cdot 4 - 3$

Step 2.6

Multiply $5$ by $3$ .

$9 + 15 - 3 + 5 \cdot 4 - 3$

Step 2.7

Subtract $3$ from $15$ .

$9 + 12 + 5 \cdot 4 - 3$

Step 2.8

Add $9$ and $12$ .

$21 + 5 \cdot 4 - 3$

Step 2.9

Multiply $5$ by $4$ .

$21 + 20 - 3$

Step 2.10

Subtract $3$ from $20$ .

$21 + 17$

Step 2.11

Add $21$ and $17$ .

$38$