1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
serious [3.7K]
3 years ago
9

Find the first term and the common ratio third term =6 and seventh term= 96​

Mathematics
1 answer:
mamaluj [8]3 years ago
6 0

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: a_n= a_1r^{n-1}

We are given: third term = 6 i,e

a_3=a_1r(3-1)\\6=a_1r^2----eq(1)

Seventh term = 96

a_7=a_1r(7-1)\\96=a_1r^6----eq(2)

Dividing eq(2) and eq(3)

\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}

So, Common Ratio r = 2

Finding First term using eq(1)

a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}

So, First term a₁ = 3/2 and common ratio r = 2

You might be interested in
90 plus what equals 395
rodikova [14]
305 plus 90= 395. Found by doing 395-90
5 0
3 years ago
Read 2 more answers
When Sam gave Clarissa 105 chocolates, Clarissa had 5 times as many chocolates as Sam. They had 504 chocolates altogether. How m
IgorLugansk [536]

Answer:

315 chocolate

Step-by-step explanation:

Let Sam's chocolate be S

Let Clariss's chocolate be C

When Sam gave Clarissa 105 chocolates, Clarissa had 5 times as many chocolates as Sam.

This can be written as:

C = 5S

The sum of their chocolate is 504 i.e

S + C = 504

Now, let us determine the chocolate of Clarissa after receiving 105 chocolate from Sam. This can be obtained as follow:

S + C = 504

But: C = 5S

S + 5S = 504

6S = 504

Divide both side by 6

S = 504/6

S = 84.

C = 5S = 5 x 84 = 420

Therefore, Clarissa have 420 chocolate after receiving 105 chocolate from Sam.

Now, to know the amount of chocolate that Clarissa has at first, we simply subtract 105 from the present amount that Clarissa have. This is illustrated below:

Amount of chocolate that Clarissa has a first = 420 – 105 = 315

Therefore, Clarissa had 315 chocolate at first.

3 0
3 years ago
Of the 8 students in the chess club, three will represent the club at an upcoming competition. How many different 3-person teams
xz_007 [3.2K]
I think that this is a combination problem. From the given, the 8 students are taken 3 at a time. This can be solved through using the formula of combination which is C(n,r) = n!/(n-r)!r!. In this case, n is 8 while r is 3. Hence, upon substitution of the values, we have

C(8,3) = 8!/(8-3)!3!
C(8,3) = 56

There are 56 3-person teams that can be formed from the 8 students. 
6 0
3 years ago
Read 2 more answers
Simplify using a table. Can someone help?
Alona [7]
The product is -10y² -19y +15.

7 0
3 years ago
Read 2 more answers
Which term describes a system with exactly one solution
vlada-n [284]
It is called a consistent dependent system
7 0
3 years ago
Other questions:
  • HELP HELP ASAP PLZZZZZZZZ I will make u brainliest!!!!!
    5·2 answers
  • The cost of a bag of chips in a vending machine is $0.85. The cost of a Gatorade in the same machine is $1.50. Kennedy spent $23
    7·2 answers
  • Triangle ABC has vertices of A(-6,7) B(4,-1), and C(-2,-9). Find the length of the median from angle B in triangle ABC.
    12·1 answer
  • An 8-pound boneless ham contains 36 servings of meat. What is the ratio in servings per pound?
    7·1 answer
  • Don’t understand:):7:8):8:):8?:8:):
    5·1 answer
  • Simplify<br><br> (4x+2)+(x-1)=
    12·1 answer
  • If y=29,find x<br><br> y=(x+2)(x-2)<br> Please show working
    11·2 answers
  • The diameter of a circle is 14 cm. Find its area in terms of \piπ.
    8·2 answers
  • I need help ASAP please. If answers right I’ll give brainey
    10·1 answer
  • Determine if the two triangles are congruent.If they are state how you know
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!