Find the Sum of the Series 5 , 10 , 15 , 20

$5$ , $10$ , $15$ , $20$

Step 1

This is the formula to find the sum of the first $n$ terms of the sequence. To evaluate it, the values of the first and $n$ th terms must be found.

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

Step 2

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 5$

Step 3

This is the formula of an arithmetic sequence.

$a_{n} = a_{1} + d (n - 1)$

Step 4

Substitute in the values of $a_{1} = 5$ and $d = 5$ .

$a_{n} = 5 + 5 (n - 1)$

Step 5

Simplify each term.

Apply the distributive property.

$a_{n} = 5 + 5 n + 5 \cdot - 1$

Multiply $5$ by $- 1$ .

$a_{n} = 5 + 5 n - 5$

Step 6

Combine the opposite terms in $5 + 5 n - 5$ .

Subtract $5$ from $5$ .

$a_{n} = 5 n + 0$

Add $5 n$ and $0$ .

$a_{n} = 5 n$

Step 7

Substitute in the value of $n$ to find the $n$ th term.

$a_{4} = 5 (4)$

Step 8

Multiply $5$ by $4$ .

$a_{4} = 20$

Step 9

Replace the variables with the known values to find $S_{4}$ .

$S_{4} = \frac{4}{2} \cdot (5 + 20)$

Step 10

Divide $4$ by $2$ .

$S_{4} = 2 \cdot (5 + 20)$

Step 11

Add $5$ and $20$ .

$S_{4} = 2 \cdot 25$

Step 12

Multiply $2$ by $25$ .

$S_{4} = 50$

Step 13

Convert the fraction to a decimal.

$S_{4} = 50$

Find the Sum of the Series 5 , 10 , 15 , 20

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