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2 years ago

The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:

Mathematics

2 answers:

just olya [345]2 years ago

8 0

Answer:

$a_{n}=2^{n}$

64 is the 6^th term

Step-by-step explanation:

Irina-Kira [14]2 years ago

5 0

Answer:

The first term as 2.

Pattern: Multiply the previous term and 2 to get the next term.

Step-by-step explanation:

The pattern is every term is 2× the previous term.

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What is the value of 5 in 3590

Xelga [282]

Answer:

500

Step-by-step explanation:

The 5 means 500. The whole number is read three thousand-five hundred-ninety

7 0

2 years ago

Lisa uses her hair dryer daily dryer uses 1500 watts. it take 10 mintes to dry her hair each time she uses it. how much would it

Volgvan

Answer:

Step-by-step explanation:

The answer is $11.55 for the week.

1) Since 1 watt is 0.001 kilowatts, 1500 watts is 1.5 kilowatts.

2) Multiply that by 7 for the week and that equals 10.5.

3) It takes her 10 minutes each day, so it takes 70 minutes per week, that is also 1.1 hours.

4) Multiply 10.5 kilowatts by 1.1 hours and you get 11.55.

5) The answer is $11.55 per week to dry Lisa's hair.

3 0

2 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

What is the exact circumference of the circle?

Arlecino [84]

I am pretty sure it is 180 degrees

5 0

3 years ago

Read 2 more answers

Which one is grater 0.584 or 0.58 or they r both equally

Jobisdone [24]

0.584 is greater than 0.58 !

8 0

3 years ago

Read 2 more answers