PLEASE help I don't understand
What are the first five terms of the sequence defined as
a(1)=3
a(n+1)=a(n)-4, for n≥1?
A) -3, -2, -1, 0, 1
B)-1, -5, -9, -13, -17
C) 3, -1, -5, -9, -13
D) 3, -1, 0, 1, 2
well, you said the first one was 3
they go down 4 at a time
so
3 , -1 .......
then -1 - 4 = -5
so
3 , -1 , -5 , .... well that is all we need
a2= 3-4= ??
a3= a2-4= ???
a4= a3-4= ....
To find the first five terms of the sequence, we can use the given formula. Let's start by finding the second term, a(2).
From the given formula, we have:
a(n+1) = a(n) - 4
Since a(1) = 3, we can substitute n = 1 into the formula to find a(2):
a(2) = a(1) - 4
Substituting 3 for a(1):
a(2) = 3 - 4
a(2) = -1
So, the second term of the sequence is -1.
Now, let's find the third term, a(3), using the same formula:
a(3) = a(2) - 4
Substituting -1 for a(2):
a(3) = -1 - 4
a(3) = -5
Now, we can continue this process to find the fourth and fifth terms.
a(4) = a(3) - 4
Substituting -5 for a(3):
a(4) = -5 - 4
a(4) = -9
a(5) = a(4) - 4
Substituting -9 for a(4):
a(5) = -9 - 4
a(5) = -13
Therefore, the first five terms of the sequence are: -3, -1, -5, -9, -13.
Therefore, the correct answer is C) 3, -1, -5, -9, -13.