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
klemol [59]
3 years ago
8

Find

ula"> in a geometric series for which S_{n} = 189, r = \frac{1}{2}, and a_{n} = 3.
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
4 0

Answer:

\displaystyle  a_{1}    = 108

Step-by-step explanation:

we are given

the sum,common difference and nth term of a geometric sequence

we want to figure out the first term

recall geometric sequence

\displaystyle S_{ \text{n}} =  \frac{ a_{1}(1 -  {r}^{n} )}{1 - r}

we are given that

  • S_n=189
  • r=\dfrac{1}{2}
  • n=3

thus substitute:

\displaystyle 189=  \frac{ a_{1}(1 -  {( \frac{1}{2} )}^{3} )}{1 -  \frac{1}{2} }

to figure out a_1 we need to figure out the equation

simplify denominator:

\displaystyle  \frac{ a_{1}(1 -  {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2}  }  = 189

simplify square:

\displaystyle  \frac{ a_{1}(1 -  {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2}  }  = 189

simplify substraction:

\displaystyle  \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2}  }  = 189

simplify complex fraction:

\displaystyle   a_{1} (\frac{7}{8} ) \div { \frac{1}{2}  }  = 189

calculate reciprocal:

\displaystyle   a_{1} \frac{7}{8}   \times 2  = 189

reduce fraction:

\displaystyle   a_{1} \frac{7}{4}   \  = 189

multiply both sides by 4/7:

\displaystyle   a_{1} \frac{7}{4}  \times  \frac{4}{7}   \  = 189 \times  \frac{4}{7}

reduce fraction:

\displaystyle   a_{1}     = 27\times  4

simplify multiplication:

\displaystyle  a_{1}    = 108

hence,

\displaystyle  a_{1}    = 108

You might be interested in
Increase 220 by 15% please
rjkz [21]
Lets do this step by step.

1st.) what is 15% as a decimal 
15% = 0.15 

2nd.) multiply 
220 x 0.15 = 33

3rd) we add that 33 and 220 since this its asking for the increase
220 + 33 = 253

Answer = 253 
6 0
2 years ago
A figure is rotated and reflected. what can u say about the new figure in relation to the original figure?
mylen [45]
The new figure is formed differently and is not the same as the other ome
8 0
3 years ago
The product of 7 and 0.04 is 0.28.<br><br> [True]<br><br> or<br><br> [False]
tino4ka555 [31]
<span>The product of 7 and 0.04 is 0.28=true</span>
6 0
3 years ago
Read 2 more answers
Which has a mass of about 10 kilograms?<br><br> Watermelon<br> Pencil<br> Car<br> Apple
Zolol [24]

Answer:

watermelon ..........................................

8 0
2 years ago
Read 2 more answers
An item is priced at $14.61. If the sales tax is 8%, what does the item cost including sales tax?
liubo4ka [24]

Answer:

(1.08)($14.61) = $15.78

4 0
2 years ago
Other questions:
  • A polygon is shown
    14·1 answer
  • Which inequality is graphed on the number line shown?
    10·1 answer
  • What is the approximate distance between the points (-5,1) and (-2,3) on a coordinate grid? Show me an example please
    5·1 answer
  • 1 quart= 4cups=1.96, Each cup coat?
    11·1 answer
  • HELP: due sep 18!!
    12·1 answer
  • To the nearest tenth, what is the area of the shaded segment when JA = 8 ft?
    5·1 answer
  • Let the universal set U = {weekdays}. If T = {Tuesday, Thursday}, what is T'?
    14·1 answer
  • A line passes through the points (-3,-1) and (-5, 4). What is the equation of the
    8·1 answer
  • PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
    10·1 answer
  • I need to know how to solve this statistics answer
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!