find the geometric means for each given sequence 6, , , 162
There seem to be some missing terms in the sequence. Assuming it is a four-term sequence, one possible solution is:
The geometric mean of 6 and 162 is sqrt(6*162) ≈ 36.
find Sn for the arithmetic series a1=16,an=48,n=6
We can use the formula for the sum of an arithmetic series:
Sn = n/2 * (a1 + an)
Plugging in the given values:
Sn = 6/2 * (16 + 48) = 3 * 64 = 192
Therefore, the sum of the arithmetic series is 192.
To find the geometric mean of a sequence, we need to find the product of all the numbers in the sequence and then take the nth root of the product, where n is the number of elements in the sequence.
In this case, the given sequence is 6, x, y, 162. Let's assume that there are four elements in the sequence.
Step 1: Find the product of all the numbers in the sequence.
Product = 6 * x * y * 162
Step 2: Take the fourth root of the product.
Geometric Mean = (Product)^(1/4)
Since we don't know the values of x and y, we cannot calculate the exact geometric mean. However, this is the general method you would use to find the geometric mean of any given sequence.