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
Xelga [282]
3 years ago
5

Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

Mathematics
1 answer:
miv72 [106K]3 years ago
7 0

<u>Hint </u><u>:</u><u>-</u>

  • Break the given sequence into two parts .
  • Notice the terms at gap of one term beginning from the first term .They are like \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} . Next term is obtained by multiplying half to the previous term .
  • Notice the terms beginning from 2nd term , 4,7,10,13 . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]

Notice the term \dfrac{1}{2^{25}} will be too small , so we can neglect it and take its approximation as 0 .

\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]

\\\implies \boxed{ S_1 \approx 1 }

\rule{200}2

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

\implies S_2=\dfrac{n}{2}[2a + (n-1)d]

Substitute ,

\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}

Hence sum = 908 + 1 = 909

You might be interested in
How many ways can first second and third place assigned
Papessa [141]

Answer:

i cannot help you get the answer to the question without more information but i can explain how to solve it, what your question is, is called a "permutation"

Step-by-step explanation:

To calculate permutations, use the equation nPr, where n is the total number of choices and r is the amount of items being selected. To solve this equation, use the equation nPr = n! / (n - r)!    , an exclimation point means the factorial, say we need the factorial of 4, we would do this 4x3x2x1 go left to right, and it is not all at once. you multiply 4 times 3 which equals 12, then multiply 12 times 2... so on and so forth

3 0
3 years ago
The distributive works for multiplication and addition. You switch the order of the problem but it doesn't change the final prod
Alja [10]

Answer:

Is there a question?

Step-by-step explanation:

If it is, by the way I look at it, To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

5 0
3 years ago
I need help ASAP!!! Please explain how to solve the answer.
Pani-rosa [81]

Answer:

Does the answer help you?

Please choose my answer as a brainliest answer and please rate.

It take a few minutes to solve your question.

8 0
3 years ago
An average Smart TV costs $500. On Black Friday, the Smart TV goes on sale for $350. By what percent did the
Alchen [17]

Answer:

30%

Step-by-step explanation:

$500-$350=150

150/500 x 100

=30%

6 0
3 years ago
5x + 3 = 23 5. 4 = 3a – 14 6. 2y + 5 = 19 i need help with this equation
mrs_skeptik [129]

Answer:

Step-by-step explanation:

    5x + 3 = 23 x=4

5. 4 = 3a – 14 a=6

6. 2y + 5 = 19 y=7

6 0
3 years ago
Other questions:
  • Divide and answer in simplest form: 5 ÷ 3 /5
    8·1 answer
  • Rectangular pieces of land 50m wide and 120m long partitioned to two parts along diagonal what is the length meter of the fence
    9·1 answer
  • Emma ran 3 miles in 28 minutes. How long would it take her to run 6 miles​
    11·2 answers
  • UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each
    8·1 answer
  • An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and
    8·1 answer
  • A circular rug has a circumference of 18.84 feet. What is the area of the rug?
    7·1 answer
  • There are 75 students in a speech contest. Yesterday 1/5 of them gave their speech. Today, 3/5 of the remaining students gave th
    14·1 answer
  • X + 6.2 10.9 can you solve it plz i need can you explain ste by step and not to long plz
    15·2 answers
  • Degree and Radian Measures
    10·1 answer
  • I have 56,552 pencils. I share it with 25 teachers. How many pencils does each teacher get?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!