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.
Similar Questions
- A prism with a square base of side length 5 cm is constructed in layers. Its height follows an arithmetic progression, increasing by 4 cm each layer. If the height reaches 16 cm in the fourth layer, what is the total volume of the prism?
Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
