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
umka21 [38]
3 years ago
6

EXAMPLE 2 Find a formula for the general term of the sequence 3 5 , − 4 25 , 5 125 , − 6 625 , 7 3125 , assuming that the patter

n of the first few terms continues. SOLUTION We are given that a1 = 3 5 a2 = − 4 25 a3 = 5 125 a4 = − 6 625 a5 = 7 3125 . Notice that the numerators of these fractions start with 3 and increase by 1 Correct: Your answer is correct. whenever we go to the next term. The second term has numerator 4, the third term has numerator 5; in general, the nth term will have numerator Incorrect: Your answer is incorrect. . The denominators are powers of 5 Correct: Your answer is correct. , so an has denominator Correct: Your answer is correct. . The signs of the terms are alternately positive and negative so we need to multiply by a power of −1. Here we want to start with a positive term and so we use (−1)n − 1 or (−1)n + 1. Therefore, an = (−1)n − 1 · Incorrect: Your answer is incorrect. .
Mathematics
1 answer:
g100num [7]3 years ago
5 0

Answer:

a_n=\dfrac{(2+n)\cdot(-1)^{n + 1}}{5^n}

Step-by-step explanation:

We are to find a formula for the general term of the sequence

\dfrac{3}{5}, -\dfrac{4}{25}, \dfrac{5}{125}, -\dfrac{6}{625}, \dfrac{7}{3125}

We are given that a_1=\dfrac{3}{5}, a_2=-\dfrac{4}{25}, a_3=\dfrac{5}{125}, a_4=-\dfrac{6}{625}, a_5=\dfrac{7}{3125} .

  • The numerators of these fractions start with 3 and increase by 1. The second term has numerator 4, the third term has numerator 5; in general, the nth term will have numerator 2+n
  • The denominators are powers of 5, so a_n has denominator 5^n
  • The signs of the terms are alternately positive and negative so we need to multiply by a power of −1. Here we want to start with a positive term and so we use (-1)^{n + 1}.

Therefore,

a_n=\dfrac{(2+n)\cdot(-1)^{n + 1}}{5^n}

You might be interested in
What is the setting for little red wagon movie
eimsori [14]

Answer:

Charleston

Step-by-step explanation:

The film then details his walks across the United States between 2007 and 2010 totaling 4,263 miles (6,861 km) to draw attention to the plight of homeless children. Filmed in and around Charleston, South Carolina in May 2010, Little Red Wagon cost a reported US$5 million to produce

3 0
3 years ago
What value should go in the empty box to complete the calculation for finding the product 73.458 × 0.39?
mr Goodwill [35]

Answer:

28.64862

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Help! Solve for x !! Use picture below
creativ13 [48]

Answer:

x=7

Step-by-step explanation:

since it is the same side length,

3x+6 = 10x-43

3x-10x = -43-6

-7x = -49

x=-49/-7=7

please mark brainliest

7 0
2 years ago
Helpp please show work!
atroni [7]

Answer:

jdukfufuufkfjkrkhjjfjctyh es 636 díajfjkrkfjkfjehjjrs en el 36 minutos

7 0
3 years ago
50 POINTS TO Awnser my question any gibberish will be reported..
muminat
You need to add the two quadratics together...

x^2+11x-6+6x^2-3x+9

7x^2+8x+3
7 0
3 years ago
Read 2 more answers
Other questions:
  • 1. What is the simplified form of (x-3)/(x^2+x-12)• (x+4)/(x^2+8x+16) ?. . 2.What is the simplified form of (x+1)/(x^2+x-6) divi
    9·1 answer
  • Rewrite as a simplified fraction.<br> 3.248
    12·2 answers
  • Round each decimal to the nearest hundredth
    5·2 answers
  • 2 1/6*3 3/2/(-5 3/2)
    9·2 answers
  • A 5,8<br> b 6,7<br> c 7,6 <br> d 8,5
    9·1 answer
  • 2. Mark deposits $600 into a savings account that earns 5% interest compounded annually for 3 years. How much money will Mark ha
    12·1 answer
  • 10. Which of these is NOT a perfect square?<br> a. 81<br> b. 100<br> C. X2<br> d. 42
    14·1 answer
  • Ms. Baranek buys trophies for field day each trophie cost $3.95 she pays $138.25 for all the trophies how many trophies does ms
    8·2 answers
  • What is m&lt;4 if m&lt;5 = (2x) and m&lt;4 = (x + 9)º? <br><br> Please
    12·2 answers
  • Select all the rational numbers
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!