All categories

2 years ago

The common ratio in a geometric series is 0.5 and the first term is 256. Find the sum of the first 6 terms in the series

Mathematics

1 answer:

Svetach [21]2 years ago

4 0

Answer:

The sum of the first 6 terms of the series is 504.

Step-by-step explanation:

Given that,

Common ratio in a geometric series is, r = 0.5

First term of the series, a = 256

We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:

$a,ar^1,ar^2,ar^3......$

The sum of n terms of a GP is given by :

$S_n=\dfrac{a(1-r^n)}{1-r}$

Here, n = 6

$S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504$

So, the sum of the first 6 terms of the series is 504.

You might be interested in

What value of x is in the solution set of 2(3x - 1) >equal to 4x - 6

klasskru [66]

Answer:

x»-2

Step-by-step explanation:

$6x - 2 \geqslant 4x - 6 \\ 2x \geqslant - 4 \\ x \geqslant - 2$

5 0

3 years ago

What is the value of x?

Ivenika [448]

32.5 degrees is the answer

8 0

2 years ago

Find the measure of 7

fredd [130]

Answer:

126 degree

Step-by-step explanation:

use alternate angles and linear pair

7 0

2 years ago

What are the solutions to the equation 2(x-3)^2=54 ?

erastova [34]

Answer:

x =(6-√108)/2=3-3√ 3 = -2.196

x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

2 • (x - 3)2 - 54 = 0

Step 2 :

2.1 Evaluate : (x-3)2 = x2-6x+9

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2x2 - 12x - 36 = 2 • (x2 - 6x - 18)

Adding 9 has completed the left hand side into a perfect square :

x2-6x+9 =

(x-3) • (x-3) =

(x-3)2 (x-3)1 =

x-3

Now, applying the Square Root Principle to Eq. #4.3.1 we get:

x-3 = √ 27

Add 3 to both sides to obtain:

x = 3 + √ 27

Since a square root has two values, one positive and the other negative

x2 - 6x - 18 = 0

has two solutions:

x = 3 + √ 27

x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

4.4 Solving x2-6x-18 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = 1

B = -6

C = -18

Accordingly, B2 - 4AC =

36 - (-72) =

108

Applying the quadratic formula :

6 ± √ 108

x = —————

Can √ 108 be simplified ?

Yes! The prime factorization of 108 is

2•2•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 108 = √ 2•2•3•3•3 =2•3•√ 3 =

± 6 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 6 ± 6 • 1.732 ) / 2

Two real solutions:

x =(6+√108)/2=3+3√ 3 = 8.196

or:

x =(6-√108)/2=3-3√ 3 = -2.196

7 0

2 years ago

Delaware was the first state to enter the Union and Hawaii was the 50th. If we order the positions of entry for the rest of the

Anna71 [15]

Answer:

State A was the <u>12th</u> state to enter the Union. State B was the <u>11th</u> state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}$

$x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}$

$x = \frac{-1 \pm 23}{2}$

$x_1 = \frac{-1 + 23}{2}$

$x_1 = 11$

$x_2 = \frac{-1 - 23}{2}$

$x_2 = -12$

The negative solution has no sense in the context of our problem, then the solution is x = 11.

5 0

2 years ago