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Dimas [21]
3 years ago
13

Write the sum using summation notation, assuming the suggested pattern continues. 2 - 8 + 32 - 128 + ...

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
4 0
This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
  an = a1*r^(n-1)

The sum is the sum of such terms.
sum=\sum\limits_{n=1}^{\infty}{2(-4)^{(n-1)}}
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Write a recursive rule for the sequence.
Vadim26 [7]

Answer:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Step-by-step explanation:

This is the fibonacci sequence with each term times x.

Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.

That is:

1x+1x=2x

1x+2x=3x

2x+3x=5x

3x+5x=8x

So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.

f(1)=1x since first term of f is 1x

f(2)=1x since second term of f is 1x

Yes, I'm naming the sequence f.

So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...

Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.

So in general f(n)=f(n-1)+f(n-2).

So the full recursive definition is:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

8 0
3 years ago
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
max2010maxim [7]

Answer:c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
if Kassidy earns 8$ per hour and Andrea earns 10$ per hour how much more in PERCENT% does Andrea make than Kassidy?
Vilka [71]
Subtract the numbers.

10 - 8 = 2

Divide it to the smaller number:

2 / 8 = 0.25

Multiply by 100:

0.25 * 100 = 25%
5 0
3 years ago
Which of the following man did not help write the federalism papers
IrinaVladis [17]

I believe the correct answer is D Aarron Burr

4 0
3 years ago
Select the equation that most accurately depicts the word problem. One-half of a certain number is 95.
Anastaziya [24]

Answer:

you would only need to add or multiply the numbers

Step-by-step explanation:

some of the equations could be-

95+ x =190

95 x 2 =190

x / 2 = 190

5 0
3 years ago
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