All categories

3 years ago

Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary.

Mathematics

1 answer:

sladkih [1.3K]3 years ago

5 0

Answer:

Answer is -759/5

Step-by-step explanation:

To find the sum of a finite geometric series, use the formula,

Sn= a1-a1r^n/ 1-r

where n is the number of terms, a1 is the first term and r is the common ratio .

common ratio = a2/a1

S8=3-3(-2/3)8 / 1-(-2/3)

S8 = 3-(-2)8/ 1+ 2/3

S8= 3-256/ 3+2/3

S8= -253/5/3

S8= -253*3/5

S8= -759/5

You might be interested in

A spacecraft travels at a speed of 5 x 10^4 miles per day. How long will it travel in 1.5 x 10^2 days?

Dimas [21]

Answer:

$7.5 \times 10^6$ miles

Step-by-step explanation:

$(5\times 10^4)\times (1.5 \times 10^2)=\\(5\times 1.5) \times (10^4 \times 10^2)=\\7.5 \times 10^6$

Hope this helps!

6 0

3 years ago

El numeral 32012(4) representado en el sistema decimal, porfavor

olya-2409 [2.1K]

Answer: El número es 902 en el sistema decimal.

Step-by-step explanation:

Supongo que tenemos el número:

32012 en base 4, y lo queremos representar en base decimal.

Entonces, usando la regla general, podemos escribir este número como:

unidades*base^0 + decenas*base^1 + centenas*base^2......

Es decir, acá tenemos:

2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902

El número es 902 en el sistema decimal.

7 0

3 years ago

there are 4 times as many snakes as turtles at biophilia if there are 26 turtles,how many snakes are at biophilia?

77julia77 [94]

To solve this, multiply the 26 turtles by 4. The final answer will be 104 snakes. Brainliest? Hope this helped!!

8 0

3 years ago

Which of the sets of ordered pairs represents a function? (1 point)

erastova [34]

The answer is only P

3 0

3 years ago

Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

5 0

1 year ago