Precalculus Examples

$\sum_{j = 1}^{6} 5 + 3 n$

Step 1

Split the summation into smaller summations that fit the summation rules.

$\sum_{j = 1}^{6} 5 + 3 n = \sum_{j = 1}^{6} 5 + 3 \sum_{j = 1}^{6} n$

Step 2

Evaluate $\sum_{j = 1}^{6} 5$ .

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Step 2.1

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 2.2

Substitute the values into the formula.

$(5) (6)$

Step 2.3

Multiply $5$ by $6$ .

$30$

Step 3

Evaluate $3 \sum_{j = 1}^{6} n$ .

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Step 3.1

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 3.2

Substitute the values into the formula and make sure to multiply by the front term.

$(3) ((n) (6))$

Step 3.3

Simplify.

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Step 3.3.1

Move $6$ to the left of $n$ .

$3 (6 n)$

Step 3.3.2

Multiply $6$ by $3$ .

$18 n$

Step 4

Add the results of the summations.

$30 + 18 n$