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
Setler79 [48]
3 years ago
7

Find the correct sum of each geometric sequence.

Mathematics
2 answers:
Alex777 [14]3 years ago
5 0
A geometric sequence with first term "a" and common ratio "r" has "nth" term:

ar^(n-1)

And the sum of a geometric sequence with "n" terms, first term "a," and common ratio "r" has the sum "a(r^n - 1)/r - 1.

1.) 765

2.) 300

3.) 1441

4.) 244

5.) 2101
grin007 [14]3 years ago
3 0

Answer:

1.765

2.301

3.1441

4.183

5.2101

Step-by-step explanation:

We are given that

1.a_1=3, a_8=384,r=2

We know that sum of nth term in G.P is given by

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

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

n=8, r=2 a=3

Therefore,S_8=\frac{3((2)^8-1)}{2-1} because r > 1

S_8=3\times (256-1)=765

1. Sum of given G.P is 765

2.a_1=343,a_n=-1,r=-\frac{1}{7}

nth term of G.P is given by the formula

a_n=ar^{n-1}

Therefore , applying the formula

-1=343\times (\frac{-1}{7}}^{n-1}

\frac{-1}{343}=(\frac{-1}{7})^{n-1}

(\frac{-1}{7})^3=(\frac{-1}{7})^{n-1}

When base equal on both side then power should be equal

Then we get n-1=3

n=3+1=4

Applying the formula of sum of G.P

S_4=\frac{343(1-(\frac{-1}{7})^4)}{1-\frac{-1}{7}} where r < 1

S_4=\frac{343(1+\frac{1}{343})}{\frac{8}{7}}

S_4=343\times\frac{344}{343}\times\frac{7}{8}

S_4=301

3.a_1=625, n=5,r=\frac{3}{5} < 1

Therefore, S_5=\frac{625(1-(\frac{3}{5})^5)}{1-\frac{3}{5}}

S_5=625\times \frac{3125-243}{3125}\times \frac{5}{2}

S_5=625\times\frac{2882}{3125}\times\frac{5}{2}

S_5=1441

4.a_1=4,n=5,r=-3

S_5=\frac{4(1-(-3)^5}{1-(-3)} where r < 1

S_5=\frac{3(1+243)}{1+3}

S_5=3\times 61=183

5.a_1=2402,n=5,r=\frac{-1}{7}

S_5=\frac{2401(1-(\frac{-1}{7})^5)}{1-\frac{-1}{7}} r < 1

S_5=\frac{2401(1+\frac{1}{16807})}{\frac{7+1}{7}}

S_5=2401\times\frac{16808}{16807}\times\frac{7}{8}

S_5=2101

You might be interested in
Please answer correctly! I will mark you as Brainliest!
andrew-mc [135]

Answer:

V = 336 ft3

Step-by-step explanation:

1/2*7*16*6

336

5 0
3 years ago
Read 2 more answers
Solve four sixths plus one third
koban [17]

Answer:

Solve four sixths plus one third

The answer is 1

4 0
2 years ago
URGENT!!!<br> Which function is shown in the graph?
katrin2010 [14]

Answer:

<h2>it's b</h2><h2>you can go with it</h2>

...........

5 0
3 years ago
Please help with this question
AlladinOne [14]

Answer:

6 years

Step-by-step explanation:

10,000 = 22,400(0.88)^t

4 0
3 years ago
I need help... on my homework it says to write each expression in radical form, or write each radical and exponential form . For
pantera1 [17]

\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{13}\implies \sqrt[2]{13^1}\implies 13^{\frac{1}{2}}

5 0
3 years ago
Other questions:
  • 6x-3(2-3x)can some one please help
    6·2 answers
  • 4/5 of a number is 32​
    12·2 answers
  • shaun plotted a point on the number line by drawing 5 equally spaced marks between 0 and 1 and placing a point on the third mark
    11·1 answer
  • Convert 150K to C degrees
    11·2 answers
  • A/b + c/b=? Simmmmmpppppllllliiiifffyyy
    13·2 answers
  • What is the length of LN?
    9·1 answer
  • Find mZEGD <br><br><br> helppppppppppp pleaseeee :))
    6·1 answer
  • Translate algebraic words to symbols.
    9·2 answers
  • Write square root of −12 ​in simplest radical form.
    13·1 answer
  • There are 30 marbles in a bag. 24 of them are blue. What percentage of the marbles are blue?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!