https://www.mathsisfun.com/algebra/sequences-sums-geometric.html
r - -3
a = -4
Xn = Xn-1 * -3 recursive
Xn = -4 (-3)^(n-1) general
= -4 , -4*-3, 12(-3) , -36 * -3
{-4, 12, -36, ...}
r - -3
a = -4
Xn = Xn-1 * -3 recursive
Xn = -4 (-3)^(n-1) general
= -4 , -4*-3, 12(-3) , -36 * -3
Let's calculate the common ratio (r) for this sequence:
r = 12 / (-4) = -3
r = -36 / 12 = -3
As we can see, the common ratio (r) is -3 for this sequence.
Now that we have the common ratio, we can establish the recursive formula for a geometric sequence. The formula takes the form: an = r * an-1, where "a" represents the term index and "n" represents the term number.
So, in this case, the recursive formula for the given sequence is:
an = -3 * an-1
To find the 5th term in the sequence, we can use the recursive formula and work our way up from the initial term.
Let's go step by step:
a1 = -4 (Given)
a2 = -3 * a1 = -3 * (-4) = 12
a3 = -3 * a2 = -3 * 12 = -36
a4 = -3 * a3 = -3 * (-36) = 108
a5 = -3 * a4 = -3 * 108 = -324
Therefore, the 5th term in the sequence is -324.
To summarize:
Recursive formula: an = -3 * an-1
5th term of the sequence: -324
Common ratio (r) can be found by dividing any term in the sequence by its preceding term.
Let's calculate the common ratio:
r = 12 / (-4) = -3
So, the common ratio (r) is -3.
The recursive formula for a geometric sequence is given by:
a(n) = a(n-1) * r
Where:
a(n) is the nth term in the sequence.
a(n-1) is the (n-1)th term in the sequence.
r is the common ratio.
Now, let's find the 5th term in the sequence using the recursive formula.
First, we know the first term of the sequence, a(1), is -4.
Now we can use the recursive formula to find subsequent terms:
a(2) = a(1) * r
= -4 * (-3)
= 12
a(3) = a(2) * r
= 12 * (-3)
= -36
a(4) = a(3) * r
= -36 * (-3)
= 108
a(5) = a(4) * r
= 108 * (-3)
= -324
Therefore, the recursive formula is a(n) = a(n-1) * (-3), and the 5th term in the sequence is -324.