5, 10, 15, ...?
Arithmetic Sequence 12th Term Calculation
The given sequence is 5, 10, 15, ...
This is an arithmetic sequence because the difference between consecutive terms is constant.
Identifying Sequence Properties
- First term ($a_1$): 5
- Common difference ($d$): $10 - 5 = 5$
- Term to find ($n$): 12
Using the Arithmetic Sequence Formula
The formula to find the $n$-th term ($a_n$) of an arithmetic sequence is:
$ a_n = a_1 + (n-1)d $
Calculating the 12th Term
Substitute the values $a_1 = 5$, $d = 5$, and $n = 12$ into the formula:
$ a_{12} = 5 + (12-1) \times 5 $
First, calculate the value inside the parentheses:
$ a_{12} = 5 + (11) \times 5 $
Next, perform the multiplication:
$ a_{12} = 5 + 55 $
Finally, perform the addition:
$ a_{12} = 60 $
Result
The 12th term of the sequence 5, 10, 15, ... is 60.
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