the 12th term of a sequence is 16 the term yo term tule is subtract 3 work out the thrid term of the sequence
Answers
Answer:
Step-by-step explanation:
First, let’s search for some kind of pattern in numbers you wrote.
15−12=3 ;
12−9=3 ;
9−6=3;
So you can get any term by substracting 3 from last one (and the first term is 15).
Let’s an be equal to n-th term.
a1=15=15−0=15−0⋅3
a2=a1−3=12=15−3=15−1⋅3
a3=a2−3=9=12−3=15−6=15−2⋅3
a4=a3−3=6=9–3=12–6=15–9=15−3⋅3
a5=a4−3=3=6−3=9−6=12−9=15−12=15−4⋅3
If you take closer look at the end of each line you can see that n-th term is just 15−(n−1)⋅3
So you can say that
an=15−(n−1)⋅3
But we can see some more patterns, on example:
12,10,8,6
Here, as you can see, you get next term by substracting 2 from last one, and the first term is 12
You can do exactly the same for this one, and you will get similiar expression:
an=12−(n−1)⋅2
Let’s try growing pattern!
5,10,15,20
Here you don’t substract, but you add ( 5 ), so:
an=5+(n−1)⋅5
Okey, as you can see all of this is similiar. They are different in one thing: in first and second pattern you had minus sign, in last one there is plus sign. Let’s change first and second pattern to have plus. What should i add to 15 to get 12 ? −3 . And what to add to 12 to get 9 ? Also −3 . So if you change all 3 into −3 and change sign from − to + you will get:
an=15+(n−1)⋅(−3)
The same for the second one:
an=12+(n−1)⋅(−2)
That thing is called . Let’s define first term as a1 .
Then a2=a1+r
a3=a2+r=a1+2⋅r
a4=a3+r=a1+3⋅r
In general:
an=a1+(n−1)⋅r
In first pattern a1=15 and r=−3 (what should i add to 1st term to get second, what should i add to 2nd term to get third, what should i add to 3rd term to get fourth etc. It all should be the same, otherwise it is not arithmetic sequence).
It is very easy to get any term, if you know r and any (other) term:
an=ax+(n−x)⋅r
To get an from ax you add r n−x times (look in first lines of this answer: to get, on example, a4 from a2 you had to add −3 two times, more precisely 4–2 times).