Find the next three terms in the geometric sequence.
5, -1, 1/5, -1/25, 1/125
To find the next term in a geometric sequence, we need to find the common ratio and then multiply it by the last term given.
The common ratio is found by dividing any term by its previous term.
For example, to find the common ratio between -1 and 5, we divide -1 by 5: -1 / 5 = -1/5.
The common ratio between the terms in this sequence is -1/5.
To find the next term, we multiply the last given term, 1/125, by the common ratio, -1/5:
1/125 * -1/5 = -1/625
Therefore, the next term in the sequence is -1/625.
To find the next term after that, we multiply -1/625 by the common ratio, -1/5:
-1/625 * -1/5 = 1/3125
So, the next term after -1/625 is 1/3125.
Similarly, to find the next term we multiply 1/3125 by the common ratio, -1/5:
1/3125 * -1/5 = -1/15625
Therefore, the next term after 1/3125 is -1/15625.
To find the next terms in the geometric sequence, we need to determine the common ratio and continue the pattern.
To find the common ratio, we divide any term by its previous term.
-1 / 5 = -1/5
The common ratio is -1/5.
Now, we can continue the pattern:
To find the next term:
1/5 * (-1/5) = -1/25
To find the second next term:
-1/25 * (-1/5) = 1/125
To find the third next term:
1/125 * (-1/5) = -1/625
Therefore, the next three terms in the geometric sequence are:
-1/25, 1/125, -1/625.
To find the next three terms in a geometric sequence, we need to identify the common ratio and then continue multiplying by that ratio.
In this sequence, the common ratio is found by dividing any term by the previous term. Let's calculate:
The common ratio (r) = (-1) / (5) = -1/5
To find the next term, multiply the last term (1/125) by the common ratio (-1/5):
(1/125) * (-1/5) = -1/625
Therefore, the fifth term is -1/625.
To find the sixth term, multiply the fifth term (-1/625) by the common ratio (-1/5) again:
(-1/625) * (-1/5) = 1/3125
Therefore, the sixth term is 1/3125.
To find the seventh term, multiply the sixth term (1/3125) by the common ratio (-1/5):
(1/3125) * (-1/5) = -1/15625
Therefore, the seventh term is -1/15625.
So, the next three terms in the given geometric sequence are: -1/625, 1/3125, -1/15625.