Find the next three terms in the following geometric sequence.
32, 48, 72, 108,…
The common ratio between the terms in the sequence is found by dividing any term by the previous term. The common ratio can also be found by dividing any term by the next term. To find the common ratio between the terms, divide 72 by 48: $\frac{72}{48}=\frac{3}{2}$. So the common ratio between the terms in the sequence is $\frac{3}{2}$. To find the next term, multiply 108 by $\frac{3}{2}$: $108\cdot\frac{3}{2}=\boxed{162}$. To find the next term after that, multiply 162 by $\frac{3}{2}$: $162\cdot\frac{3}{2}=\boxed{243}$. To find the next term after that, multiply 243 by $\frac{3}{2}$: $243\cdot\frac{3}{2}=\boxed{364\frac{1}{2}}$.
To find the next three terms in the geometric sequence, we need to identify the common ratio first. We can do this by dividing any term by its previous term. Let's choose the second and first terms, 48 and 32:
48 / 32 = 1.5
The common ratio is 1.5.
Now, we can use the formula for the nth term of a geometric sequence:
Tn = a * r^(n-1)
where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number.
Using the given terms, the sequence can be represented as:
T1 = 32
T2 = 32 * 1.5 = 48
T3 = 48 * 1.5 = 72
T4 = 72 * 1.5 = 108
Now, let's find the next three terms:
T5 = 108 * 1.5 = 162
T6 = 162 * 1.5 = 243
T7 = 243 * 1.5 = 364.5
Therefore, the next three terms in the geometric sequence are 162, 243, and 364.5.
To find the next three terms in the geometric sequence, we need to identify the common ratio between the terms. The common ratio (r) can be found by dividing any term in the sequence by its preceding term.
Let's find the common ratio for this sequence by dividing the second term (48) by the first term (32):
r = 48/32 = 3/2 = 1.5
Now that we know the common ratio, we can find the next three terms by multiplying the last term (108) by the common ratio (1.5).
To find the next term after 108, multiply 108 by 1.5:
Next term = 108 * 1.5 = 162
To find the second next term, multiply the previous term (162) by 1.5:
Second next term = 162 * 1.5 = 243
To find the third next term, multiply the previous term (243) by 1.5:
Third next term = 243 * 1.5 = 364.5
Therefore, the next three terms in the geometric sequence are:
162, 243, 364.5