Two terms in a geometric sequence are a3=729 and a4=243.What is the first term of the sequence, and what is the recursive rule that describes the sequence?
Answers
The first term of the given sequence (a) = 6561
Step-by-step explanation:
Let the first term = a and common difference = d
Given,
= 729 and
= 243
To find, the first term of the given sequence (a) = ?
We know that,
The nth term of a G.P.
The 3rd term of a G.P.
⇒ = 729 ..............(1)
The 4th term of a G.P.
⇒ = 243 ..............(2)
Dividing equation (2) by (1), we get
=
⇒
Put in equation (1), we get
= 729
⇒ = 729
⇒ a = 9 × 729 = 6561
∴ The first term of the given sequence (a) = 6561
Final answer:
The first term of the geometric sequence is 6561 and the recursive rule of the sequence is a(n) = a(n-1) * 1/3.
Explanation:
In a
geometric sequence
, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the
common ratio
. In your case, you are given the third term, a3=729, and the fourth term, a4=243 in the sequence. We know that in a geometric sequence, any term divided by the previous term gives the common ratio. So 243/729 = 1/3, which is the common ratio, r.
Now, to find the first term, we use the provided values and the formula for the nth term in a geometric sequence which is a = a3 / r^n, where a is the first term, r is the common ratio, and n is the term number. Therefore, to find the first term, we go back two steps from the third term (729) dividing by 1/3 each time: (729/1/3) = 2187 (which is the second term) and again (2187/1/3) = 6561 (which is the first term).
So, the first term, a1=6561, and the recursive rule that describes this sequence is a(n) = a(n-1) * 1/3
Learn more about Geometric Sequence here:
#SPJ12
Related Questions
This is my first time, but my question is what is 7/8 of 20?
What is a rate in math ?the question -------->what was the heart rate for the students with the lowest heart rate? 78,80,82,83,84,85,86,87,88,90
What is the angle of B. Round your answer to the nearest hundredth
The avocado own a 1/4 acre orchard. Two fifths of the orchard is planted in orange trees. What fraction of an acre in planted in orange trees
Answers
Answer: the other rational number is 118/19
Answer:
-118/19
Step-by-step explanation:
let x, y = the two rational numbers, respectively.
What do we know?
- x + y = -7
- x = -15/19
Step one: Plug in the values:
-15/19 + y =-7
Step two: Isolate the variable by adding 15/19 on both sides
y = -7 +15/19
Step three: Simplify the right side
Use basic addition to add the two numbers:
y = - 118/19
Answers
or
65 x 1.5 = 97.5...
just remember to keep to the basics!
Answers
Answer: The last one
Step-by-step explanation:
I think this because the graph starts from H the number of hours studied and when u add the numbers and divide them up which gives you the equation 65 + 50 . Any questions please text me. Have a nice day.
Answers
Answers
18.
10(b - 6)
Distributive property.
10b - 60.
20.
7(8 + y)
Distributive property.
56 + 7y.
22.
9(2n + 1)
Distributive property.
18n + 9
24.
18(5 - 3w)
Distributive property.
90 - 54w
26.
7(8 + x + 2)
Distributive property.
56 + 7x + 14
Combine like terms.
70 + 7x
28.
6(10 + z + 3)
Distributive property.
60 + 6z + 18
Combine like terms.
78 + 6z
30.
25(x - y)
Distributive property.
25x - 25y
32.
13(n + 4 + 7m)
Distributive property.
13n + 52 + 91
Answers
100g • 10 = 1000g
Isaiah would need to put 10 100 gram weights on the scale in order for it to equal 1 kilogram.
Final answer:
Isaiah would need to place 10 units of 100 gram weights on the balance scale to counterbalance the kilogram. This is because a kilogram equates to 1000 grams and each weight is 100 grams.
Explanation:
To determine how many 100 gram weights are needed to balance a scale with a kilogram on the other side, we first need to understand that a kilogram (kg) is equivalent to 1000 grams (g). This is based on the metric system, where the prefix 'kilo-' signifies a factor of 1000.
Therefore, if Isaiah has a kilogram on one side of the scale, he has a mass of 1000 grams to balance. Given that the weights he is using are each 100 grams, he would need to use 10 of these weights to balance the mass on the scale. This because 100 (grams per weight) times 10 (weights) equals 1000 grams which is equal to the kilogram placed on the other side.
Learn more about Weight Balance here:
#SPJ2