Find the next three terms in the following geometric sequence.
4, −12, 36, −108,…
To find the common ratio, we divide the second term by the first term and the third term by the second term.
Common ratio = -12/4 = -3
Third term = 36 * -3 = -108
So the next three terms in the sequence are:
-108 * -3 = 324
324 * -3 = -972
-972 * -3 = 2916
To find the next three terms in the geometric sequence, we need to determine the common ratio (r).
To find the common ratio, we divide any term by its previous term.
Let's divide the second term by the first term:
r = (-12) ÷ 4 = -3
Now, let's divide the third term by the second term:
r = 36 ÷ (-12) = -3
Since both divisions give us the same result, we can say that the common ratio (r) is -3.
To find the next terms, we can multiply each term by -3.
The fourth term is obtained by multiplying the third term by -3:
-108 × (-3) = 324
The fifth term is obtained by multiplying the fourth term by -3:
324 × (-3) = -972
The sixth term is obtained by multiplying the fifth term by -3:
-972 × (-3) = 2,916
Therefore, the next three terms in the geometric sequence are 324, -972, and 2,916.
To find the next three terms in the given geometric sequence, we need to determine the common ratio first.
The common ratio (r) is found by dividing any term by its previous term. Let's calculate it:
r = (-12) / 4
r = -3
Now that we have the common ratio, we can use it to find the next three terms.
To find the next term in the sequence, we multiply the last term by the common ratio:
36 * (-3) = -108
The next term is -108.
To find the term after that, we again multiply the previous term (-108) by the common ratio:
-108 * (-3) = 324
The term after -108 is 324.
Similarly, to find the next term, we multiply the previous term (324) by the common ratio:
324 * (-3) = -972
The next term is -972.
Therefore, the next three terms in the sequence are -108, 324, and -972.