All categories

3 years ago

What is the sum of the geometric sequence 3,12,48... if there are 8 terms?

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

6 0

Answer:

C) 65,535

Step-by-step explanation:

You can add up the 8 terms ...

3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

Estimating

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

Using the formula

You know the formula for the sum of a geometric sequence is ...

S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

You might be interested in

What is the midpoint

Tom [10]

Its a.

Lol taking forever to do stuff is fun.

8 0

3 years ago

The vertex is at (-1,-3) move it to (8,10) on the coordinate grid.

givi [52]

Right 9 spaces and up 13 spaces

5 0

3 years ago

Help help legit answers only

Ne4ueva [31]

Answer:

x ≈ 46.7°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = $\frac{opposite}{hypotenuse}$ = $\frac{OP}{NP}$ = $\frac{4}{5.5}$ , then

x = $sin^{-1}$ ( $\frac{4}{5.5}$ ) ≈ 46.7° ( to the nearest tenth )

6 0

3 years ago

Read 2 more answers

What is 13/15 rounded to the nearest decimal?

RUDIKE [14]

$\frac{13}{15} = 13 : 15 = 0,8(6)$

6 0

3 years ago

Find the kissing lengths of the sides of the triangle.

alina1380 [7]

Answer: The last option.

Step-by-step explanation:

The triangle shown in the figure attached is a right triangle.

1. You can calculate the lenght a as following:

$sin\alpha=\frac{opposite}{hypotenuse}$

$opposite=a\\hypotenuse=6in\\\alpha=30\°$

Substitute values and solve for a. Then, you obtain:

$sin(30\°)=\frac{a}{6in}\\a=6in*sin(30\°)\\a=3in$

2. You can calculate the lenght b as following:

$cos\alpha=\frac{adjacent}{hypotenuse}$

$adjacent=b\\hypotenuse=6in\\\alpha=30\°$

Substitute values and solve for b. Then, you obtain:

$cos(30\°)=\frac{b}{6in}\\b=6in*cos(30\°)$

$b=3\sqrt{3}in$

3 0

3 years ago