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
Leviafan [203]
2 years ago
13

Find the sum of the first 9 terms in the following geometric series.

Mathematics
2 answers:
Bezzdna [24]2 years ago
7 0

Answer:

Sum of 9terms = 68,887

Step-by-step explanation:

Sum nth term of a GP series is Sn = a(r^n -1)/(r-1)

where a = first term

r = common ratio = Tn/Tn-1

n = nth of term

Therefore for 7,21 ,63 +...

a = 7

r = 21/7 = 3

I.e

Sum of 9 terms = 7 x (3^9-1)/(3-1)

=7 x (19683-1)/2

7 x 19682/2

= 7 x 9841

= 68,887

Sum of 9terms = 68,887

Jlenok [28]2 years ago
6 0

Answer:

The sum of first 9 terms of the given sequence = 68887

Step-by-step explanation:

Given sequence:

7+21+63......

The given sequence is a geometric sequence as the successive numbers bear a common ratio.

The ratio can be found out by dividing a number by the number preceding it.

For the given geometric sequence common ratio r can be given as:

r=\frac{21}{7}=3

The sum of a geometric sequence is given by:

S_n=\frac{a_1(r^n-1)}{r-1}       when r>1

and

S_n=\frac{a_1(1-r^n)}{1-r}      when r

where, S_n represents sum of nterms, n representing number of terms and r represents common ratio and a_1 represents the first term.

Since for the given geometric sequence has a common ratio =3 which is >1, so we will use the first formula for sum to calculate the sum of first 9 terms.

Plugging in the values to find sum of first 9 terms.

S_9=\frac{7(3^9-1)}{3-1}  

S_9=\frac{7(19683-1)}{3-1}  

S_9=\frac{7(19682)}{2}

S_9=\frac{137774}{2}

∴ S_9=68887  

Thus sum of first 9 terms of the given sequence = 68887 (Answer)

You might be interested in
The sides of a square are 3 2/7 inches long.<br> What is the area of the square?
vredina [299]
Area is just height times width so if it’s a square all sides are equal so you do 3 2/7 time 3 2/7 and get 10.796 in^2
3 0
3 years ago
Brittany buys 2.55 pounds of turkey for $5.96 per pound and 3.7 pounds of
Galina-37 [17]

Answer:

Brittany needs another $3.7405.              

Step-by-step explanation:

Per pound Cost of turkey = $5.96 per pound

The amount Brittany buys the turkey = 2.55 pounds

Brittany's cost for turkey = 2.55 × $5.96 = $15.198

Per pound cost for cheese = $3.35 per pound

The amount Brittany buys the cheese = 3.7 pounds

Brittany's cost for cheese = 2.55 × $3.35 = $8.5425

So,

Brittany's total cost = Turkey cost + Cheese cost

                                = $15.198 + $8.5425

                                = $23.7405

As brittany gave the clerk 20 dollars.

So, the amount she further needs will be:

$23.7405 - $20 =  $3.7405

Therefore, Brittany needs another $3.7405.                                                                      

8 0
2 years ago
0.63 + _____ = $1.00*
Sliva [168]
The answer would be 0.37.
4 0
3 years ago
Read 2 more answers
Help asap!!!!!!Order the number below from least to greatest
OLEGan [10]

Answer:

B.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
8 batteries cost £3.99 how much does 1 cost
NemiM [27]

Answer:

1 battery cost .49875 cents, but .50 rounded

Step-by-step explanation:

Divide 3.99 by 8 and you will get .49875

4 0
3 years ago
Read 2 more answers
Other questions:
  • How is this wrong? I cant find it out, google says it is -7 but why?
    6·2 answers
  • 3. Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.
    10·1 answer
  • What is the y in the equation? 15-y-3y=17
    12·1 answer
  • How many inches are in 3 feet?
    7·2 answers
  • There are 80 sixth graders at Wilson Middle School. Only 40% of the sixth g
    9·1 answer
  • A bag of marbles contains 4 red
    14·1 answer
  • Find the slope and y intercept of 2y +8 = 6x + 4
    12·2 answers
  • 20 - 4 TIMES 4 DIVIDE 2 + 3
    7·2 answers
  • I watched a video and didn't get my free answer, can I have some help,
    15·1 answer
  • The attempt to recapture the Holy Land from the Muslims is called the .
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!