find k, given that the following are consecutive term of a geometric sequence.
k,k+8,9k
thank u
To find the common ratio, we can divide any term by its previous term in the sequence since the terms are consecutive. So, let's divide the second term (k + 8) by the first term (k):
(k + 8) / k
To simplify this, we can divide each term of the numerator by k:
1 + 8/k
Since this is a geometric sequence, the common ratio is the same throughout. Therefore, we can also divide the third term (9k) by the second term (k + 8):
9k / (k + 8)
Now, we can set up an equation to find k. Since the common ratio is the same, we can equate the two expressions we obtained:
1 + 8/k = 9k / (k + 8)
Next, we can cross-multiply to remove the denominators:
(k + 8)(1 + 8/k) = 9k
Simplifying this expression:
k + 8 + 8k/k = 9k
k + 8 + 8 = 9k
k + 16 = 9k
Next, move all terms involving k to one side to solve for k:
16 = 9k - k
16 = 8k
Finally, divide both sides by 8 to isolate k:
k = 2
Therefore, k is equal to 2.
For a GS
(k+8)/k = 9k/(k+8)
cross-multiply and arrange as a quadratic.
You should get two different values for k.