determine whether each sequence is geometric. If so, identify the common ration and find the next two terms. 1,1/2,1/4,1/8
Yes, the sequence is geometric.
The common ratio is found by dividing any term by the previous term. For example:
1/2 ÷ 1 = 1/2
1/4 ÷ 1/2 = 1/2
1/8 ÷ 1/4 = 1/2
So the common ratio is 1/2.
To find the next two terms:
1/16 = (1/8) * (1/2)
1/32 = (1/16) * (1/2)
So the next two terms are 1/16 and 1/32.
is this correct
Yes, that is correct.
To determine whether a sequence is geometric, we need to check if there is a common ratio between consecutive terms. Let's examine the given sequence: 1, 1/2, 1/4, 1/8.
To find the common ratio, we can divide any term by its preceding term. Let's consider the second term divided by the first term:
(1/2) / 1 = 1/2
Now let's find the common ratio between the third term and the second term:
(1/4) / (1/2) = 1/4 * 2/1 = 1/8
Finally, let's find the common ratio between the fourth term and the third term:
(1/8) / (1/4) = 1/8 * 4/1 = 1/32
Since the common ratio between consecutive terms is the same (1/2), we can conclude that the given sequence is geometric.
To find the next two terms, we can continue multiplying by the common ratio:
To find the fifth term:
(1/8) * (1/2) = 1/16
To find the sixth term:
(1/16) * (1/2) = 1/32
Therefore, the next two terms in the sequence are 1/16 and 1/32.