Answer:
What is the first term of this sequence? 7
To get to the next term you would add 3.
This means that there is a common difference of 3.
Austin will have 28 lizards after 8 weeks.
Explanation:
Austin has 7 pet lizards and each week he adds 3 more.
So, we can see that the first term of the sequence is 7.
The next term of the sequence is the number of lizards after 1 week. This can be calculated as
7 + 3 = 10
Therefore, to get the next term you would add 3.
This number that we add is a common difference, so the common is 3.
the explicit form of the arithmetic equence has the following form
an = a0 + d(n-1)
Where an is the nth term, a0 is the first term and d is a common difference. Replacing a0 = 7 and d = 3, we get
an = 7 + 3(n-1)
So, to find the number of lizards after 8 weeks, we need to replace n by 8, so
an = 7 + 3(8-1)
an = 7 + 3(7)
an = 7 + 21
an = 28
Therefore, the answers are:
What is the first term of this sequence? 7
To get to the next term you would add 3.
This means that there is a common difference of 3.
Austin will have 28 lizards after 8 weeks.