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

Answers

Answer 1

Hint :-

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

Solution :-

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

[tex]\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}[/tex] .

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

[tex]\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] [/tex]

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

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

[tex]\\\implies \boxed{ S_1 \approx 1 }[/tex]

[tex]\rule{200}2[/tex]

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

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

Substitute ,

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

Hence sum = 908 + 1 = 909


Related Questions

Please help me with these thanks!! :)

Answers

Answer:

this one is rational and real :)

what are your recommendations about augmented learning​

Answers

Answer:

Augmented learning is an on-demand learning technique where the environment adapts to the learner. By providing remediation on-demand, learners can gain greater understanding of a topic and stimulate discovery and learning.

Augmented learning is closely related to augmented intelligence and intelligence amplification.

Augmented learning is an on-demand learning technique where the environment adapts to the learner. By providing remediation on-demand, learners can gain greater understanding of a topic and stimulate discovery and learning.

Hope this helps you

what the example of constant and variable?​

Answers

Answer:

A constant is a defined value often portrayed as a number.

A variable is a value that can change and is often represented as a letter.

Step-by-step explanation:

For example:

In the equation ? = 10x + 3y + 17

10, 3, and 17 are all constants.

X and Y are both variables.

To reiterate, constants are known values that can NOT change while variables are unknown values that can change!

Simplify the following square rots.When necessary, write the square root using the “WIRIS editor” button;

Answers

Answer:

[tex]3\sqrt{9}[/tex]

Step-by-step explanation:

[tex]\sqrt{ab}= \sqrt{a} *\sqrt{b}\\\\\sqrt{99}=\sqrt{9*11}\\\\=\sqrt{9}*\sqrt{11}\\=3\sqrt{11}[/tex]

Select the correct statement in the table.
Given that r and s are both irrational numbers, determine which statement is true.

Answers

Answer:

Below.

Step-by-step explanation:

The value of r + x is always irrational.

The value of r. s is sometimes irrational:

- for example √2 * √3 = √6 which is irrational,

but √3 * √3 = √9 = 3 which is rational.

It cost adults $7 to get into the fair and it cost children under 11 years old $4. What does it cost for 8 adults and 4 children to get into the fair?
A $82
B $84
C $72
D $76

Answers

Answer is C 72 dollars

Answer:$72

Step-by-step explanation:7*8=56

4*4=16

56+16=72

what is 7 times zero and eight tenths

Answers

Answer: 5.6

Step-by-step explanation:

8x7=56

Move the decimal from 56 once to the left because there is 1 number behind the decimal.

Solve: 1/3x + 7 = 15

Answers



See below for solution

If the sides of a square measure 9units, then find the length of the diagonal.

Answers

Answer:

12.72792

Step-by-step explanation:

d = √2a = √2 x 9 = 12.72792

Sorry, I don't have too much time to explain the question but I hope this helps!

81a^2x+9a^2y-90bx-10by

Answers

1. Factor out 9a^2 from the expression
9a^2 x(9x+y) - 90bx - 10by

2. Factor out -10b from the expression
9a^2 x(9x+y) - 10b x(9x+y)

3. Factor out 9x + y from the expression
(9x+y)x(9a^2 - 10b)

Solution: (9x+y)x(9a^2 - 10b)

irreducible fraction of -30/40​​

Answers

Answer:

-3/4

Step-by-step explanation:

An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered).

so

-30/40 =

-3/4

51661-61661+611×5561×58
Solve.​

Answers

Answer:

=197060718

Step-by-step explanation:

51661−61661+(611)(5561)(58)

=−10000+(611)(5561)(58)

=−10000+(3397771)(58)

=−10000+197070718

=197060718

5t+8=43
Pleas some one explain I do not understand.

Answers

Subtract 8 from both sides so u get 5t=35 then u have to isolate t, and to do that to divide 5 on both sides. Ur answer is 7

Answer:

7

Step-by-step explanation:

5 times 7 is 35.

35 plus 8 is 43.

Find the distance between each pair of points.
(-2,-3), (8,-1)

How do I find the difference? Due today!

Answers

I HOPE IT WILL HELP YOU.

Thank you.

I need help with #4 and #5​

Answers

Answer:

Step-by-step explanation:

Help help help help pleaE

Answers


The answer is 3,000=600*5

How many tens are in 20,000? (Answer in simple words!) Example: "38 tens", or "48 tens"

Answers

2000 tens are in 20000

93 divided by 5932 long division

Answers

Answer:

63 73/93 (steps are in the attached file)

Step-by-step explanation:

Simplify x ^8/ x ^6 ​

Answers

Answer:

[tex]\displaystyle \frac{x^8}{x^6} = x^2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Exponential Property [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{x^8}{x^6}[/tex]

Step 2: Simplify

Exponential Rule [Dividing]:                                                                             [tex]\displaystyle \frac{x^8}{x^6} = x^{8 - 6}[/tex][Exponents] Subtract:                                                                                       [tex]\displaystyle \frac{x^8}{x^6} = x^{2}[/tex]

Which system of linear inequalities is represented by
the graph?

HELPPP Please!!!

Answers

The correct answer is the first option.

Y ≥ 1/3x + 3 and 3x - y > 2

Please mark my answer as the Brainliest if you find this helpful :)

John has 3 different colored tiles. (red, blue
and green). He wants to put them into
different orders to make a pattern. How many
different patterns can he make?

Answers

Answer:you can make around 3

Step-by-step explanation:

john can make 3 different patterns because he has 3 colors for example...

pattern 1:green,red,blue

pattern 2:red,blue,green

pattern 3:blue,red,green

keep going you might find more..good luck!

find x and y ILL GIVE BRAINLIESTTTT

Answers

Answer:

y =90° x =70°

Step-by-step explanation:

Answer:

x = 70° , opposite angles of the same line with angle 70.

sum of interior angles of trapezium is 360°.

y + 70° + 90° + 110° = 360°

y = 90°

(sorry for login question pls help )

Fit Data to a line

When using empirical data ( data and information collected by scientists in an experiment ), sometimes, that data will not form a perfect line on a graph. when this happens, the line that is created using a linear regression is known as the " line of best fit " the following speed data was collected from a car moving with a constant acceleration.

1 - what is the line of best fit for this data? perform a linear regression on this table to find the equation .


2 - based on your equation, what was the car's approximate initial velocity (at time = 0) ?

3 - if the car continued at the same acceleration (meaning the slope of the line does not change), how fast would it be going in 15 seconds ? ​

Answers

Using a linear regression calculator, the best fit line, initial velocity and the velocity of the car after 15 seconds is :

y = 3.64x + 5.7 Initial Velocity = 5.7 m/s Velocity after 15 seconds = 60.3 m/s

Using technology, the linear regression equation obtained by fitting the data is :

y = 3.64x + 5.7

x = times(seconds) ; y = velocity(m/s)

The approximate velocity at time = 0 ; x = 0 :

y = 3.64(0) + 5.7

y = 0 + 5.7

y = 5.7 m/s

3.) Velocity after 15 seconds :

At time, x = 15 seconds

y = 3.64(15) + 5.7

y = 60.3 m/s

Therefore, the velocity of the car after 15 seconds is 60.3 m/s

Learn more :https://brainly.com/question/18405415

If B = -p + 10p2 and C = 2p + 7, find an expression that equals B + 3C in
standard form.

Answers

Answer:

10p^2 + 5p + 42 = b+3c

Step-by-step explanation:

b = -p + 10p^2

c = 2p + 7

b + 3c = 5p + 10p^2+ 42

PLEASE SHOW STEPS // -5 (2b + 7) + b < -b - 11

Answers

Answer:

b < -11

Step-by-step explanation:

-5 X 2b = -10b + -35 +b

-10b + 35 + b < -b -11

-b -b

cancel out the b

-10b + 35 < -11

-35 < - 35

-10b <-11

-10 < -10

b < -11 and that's your answer

What are the greatest common divisors of the pairs of integers?

Answers

Answer:5

Step-by-step explanation:

Answer two questions about Equations
A
AA and
B
BB:
A
.
3
(
x
+
2
)
=
18
B
.
x
+
2
=
18

A.
B.




3(x+2)
x+2


=18
=18


1) How can we get Equation
B
BB from Equation
A
AA?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
Multiply/divide both sides by the same non-zero constant

(Choice B)
B
Multiply/divide only one side by a non-zero constant

(Choice C)
C
Rewrite one side (or both) by combining like terms

(Choice D)
D
Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
Yes

(Choice B)
B
No

Answers

Answer:

choice B is the answer be cause you're only dividing one side by 3

and no because if you actually solve both equations separately, the answers are not the same

what is the math pattern

Answers

Math patterns are sequences that repeat according to a rule or rules. In math, a rule is a set way to calculate or solve a problem.
Hope it Helps

Fresh and easy breath lozenges have only two 3/4 cal piece how many calories are in a pack of 16 lozenges

Answers

2.75x16=44 calories

HELPPPPPPPPPPPPPPPPPPPPPPP

Answers

Domain: {13,17,22,2533} Range: {33,25,22,17,17}
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