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Murljashka [212]
2 years ago
12

Find the 12th term of an AP of the form 7, 12, 17, 22

Mathematics
1 answer:
Nostrana [21]2 years ago
6 0

Answer:

27

Step-by-step explanation:

The rule will be

Ni=(i-1)*5+2

  • i=1 → N=(1–1)*5+2=0*5+2=0+2=2
  • i=2 → N=(2–1)*5+2=1*5+2=5+2=7
  • i=3 → N=(3–1)*5+2=2*5+2=10+2=12
  • i=4 → N=(4–1)*5+2=3*5+2=15+2=17
  • i=5 → N=(5–1)*5+2=4*5+2=20+2=22
  • i=6 → N=(6–1)*5+2=5*5+2=25+2=27

________________

Learn more about arithmetic sequences:

  • brainly.com/question/6561461
  • brainly.com/question/503167

#SPJ2

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Svetradugi [14.3K]

Answer: c

Step-by-step explanation:

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3 years ago
What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Trava [24]

Answer:

\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}

Step-by-step explanation:

The explicit formula for a geometric sequence:

a_n=a_1r^{n-1}

a_n - n-th term

a_1 - first term

r - common ratio

r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}

We have

a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...

The common ratio:

r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}

<h2>It's not a geometric sequence.</h2>

If a_3=-\dfrac{1}{16} then the common ratio is r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}

Put to the explicit formula:

a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}

Put a_n=\dfrac{1}{1024} and solve for <em>n </em>:

-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1

\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6

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3 years ago
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Answer:

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Step-by-step explanation:

This is a 30 60 90 triangle. To get from 3 rad 3 to x you need to divide rad 3 which gives you 3.

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