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
Ad libitum [116K]
3 years ago
6

The second term in a geometric series is 10, and the seventh term is 10,240. Find the sum of the first six terms.

Mathematics
1 answer:
just olya [345]3 years ago
5 0

Answer:

The sum of the first 6 terms is 3,412.5.

Step-by-step explanation:

The second term of the geometric series is given by:

a_{2}=a_{1}*r

Where a1 is the first term and r is the common ratio. The seventh term can be written as a function of the second term as follows:

a_{7}=a_{1}*r^{6} \\a_{7}=a_{2}*r^{5} \\10,240 = 10*r^{5}\\r=\sqrt[5]{1024} \\r = 4

The sum of "n" terms of a geometric series is given by:

a_{1} = \frac{10}{4} = 2.5\\S_{n}=a_{1}(\frac{r^{n}-1 }{r-1})\\S_{6}=2.5(\frac{4^{6}-1 }{4-1})\\S_{6}=3,412.5

The sum of the first 6 terms is 3,412.5.

You might be interested in
Which is the best approximation for the value 140
zzz [600]
140 is a composite number. Factor pairs: 140 = 1 x 140, 2 x 70, 4 x 35, 5 x 28, 7 x 20, 10 x 14. Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. Prime factorization: 140 = 2 x 2 x 5 x 7, which can also be written 140 = 2² x 5 x 7
4 0
3 years ago
Please help me i really need help ok i need real answer
krek1111 [17]

Answer:

The last answer choice.

Step-by-step explanation:

8/10 is equal to 0.80, so that's the answer! Hope it helps!

5 0
2 years ago
Read 2 more answers
A customer buys a dress that has an original price of $38. The dress is discounted 25%. The customer pays 6% sales tax on the di
salantis [7]

Answer:

dress? or address?

Step-by-step explanation:

5 0
3 years ago
15 POINTS!! I NEED TO KNOW THE ANSWER WITHIN 2 HOURS!!! PLEASE HELP!!
iogann1982 [59]
<h3>Answer: x*a^2 or a^2*x</h3>

======================================

Work Shown:

a^(b+2) = a^b*a^2 ... break up the exponent

a^(b+2) = x*a^2 ... replace a^b with x

We don't know the value of 'a' nor the value of x, so we cannot evaluate further. This is the same as a^2*x because order of multiplication does not matter. For example, 2*3 = 6 and 3*2 = 6, so 2*3 = 3*2.

8 0
3 years ago
Read 2 more answers
4x+4 =<br> What is the answer to this please help
maw [93]

Answer:4(x+1)

Step-by-step explanation:

4x+1

3 0
2 years ago
Other questions:
  • You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
    14·1 answer
  • What is the answer to -3x+5= -16
    8·2 answers
  • Find the angle measurement of x.
    9·2 answers
  • Buying a new car can create a financial challenge because car
    7·1 answer
  • How to use the distributive law to factor 2a + 2b?
    14·1 answer
  • What is the range of f(x) = ( 3/4 ) x - 4?
    8·1 answer
  • Please help me with these two questions
    11·1 answer
  • Please help thank youu
    8·1 answer
  • Determine a series of transformations that would map polygon ABCD onto polygon A’B’C’D’?
    6·1 answer
  • Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 d
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!