Answer:
a) find common ratio = 3
b) calculate 10th term = 78732
c) k = 7
Step-by-step explanation:
A geometric sequence has second term 12 and fifth term 324.
a) find common ratio
Common ratio = r
Hence
We solve for this below:
r = cube root(fifth term/second term)
r = cube root (324/12)
r = cube root (27)
r = 3
Therefore, the common ratio = 3
b) calculate 10th term
The formula for a geometric sequence is given as:
an = ar^n-1
Where
a = First term
r = Common ratio = 3
n = Nth term = 10
Step 1
We have to find the first term
Common ratio = Second term/First term
Common ratio = 3
Second term = 12
Hence:
3 = 12/x
Cross Multiply
3x = 12
x = 12/3
x = 4
Hence , First term = 4
Step 2
We find the 10th term
an = ar^n-1
a10 = 4 × 3^10 - 1
a10 = 4 × 3⁹
a10 = 4 × 19683
a10 = 78732
Therefore, the 10th term = 78732
c) the kth term is the first term that is greater than 2000. Find the value of K
For kth term,
ak = ar^k-1 >2000
a = 4, r = 3
Hence
4 × 3^k-1 > 2000
We divide both sides by 4
4 × 3^k-1/4 > 2000/4
3^k-1 > 500
We take the logarithm of both sides
log 3^k-1 > log 500
k-1 log 3 > log 500
Divide both sides by log 3
k-1 log 3/log 3 > log 500/log 3
k - 1 > 5.6567800693
k > 5.6567800693 + 1
k > 6.6567800693
k = 7
Therefore, k = 7
Answer:
Lol he got it in spanish
Step-by-step explanation:
Well, 15% of 45 is 3, so in 4 minutes, the submarine will be 12 feet deep.
Answer:
Best approximation for the circumference of the plate = 18.84 inches
Step-by-step explanation:
Given in the question,
radius of a plate = 3 inches
π = 3.14
To find,
circumference of the plate.
As we know that formula to calculate circumference of a circle given radius
<h2>
2 π r</h2>
2 (π) (3)
2 (3.14) (3)
18.84 inches
So the circumference or perimeter of area = 18.84 inches
<h2>
</h2>
I believe it would be 12, I believe this because its states that it is TWICE as long therefore is made from the same metal so 6x2=12
