Find a geometric sequence in which the 6th term is 28 and 10th term is 448
To find a geometric sequence, we need to find the common ratio, denoted as 'r', which is the ratio between consecutive terms.
Let's call the first term of our geometric sequence 'a'.
We are given that the 6th term is 28, so we can write:
a * r^5 = 28 -------- (equation 1)
We are also given that the 10th term is 448, so we can write:
a * r^9 = 448 -------- (equation 2)
To solve this system of equations, we can divide equation 2 by equation 1 to eliminate 'a':
(a * r^9) / (a * r^5) = 448 / 28
This simplifies to:
r^4 = 16
Taking the fourth root of both sides:
r = ±2
Now that we have the value of 'r', we can substitute it back into equation 1 to find 'a':
a * 2^5 = 28
32a = 28
a = 28/32
a = 7/8
So, the first term of the geometric sequence is 7/8 and the common ratio is ±2.
Therefore, the geometric sequence can be:
7/8, 7/4, 7/2, 7, 14, 28, 56, 112, 224, 448