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4 years ago

What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …

Mathematics

1 answer:

Alex787 [66]4 years ago

6 0

Answer:

A term at position n can be expressed as \[2*3^{n-1}\]

Step-by-step explanation:

The given geometric sequence is 2, 6, 18, 54, …

Starting term = 2

Second term = 6

So second term is 3 times the first term.

Similarly, Third term = 18

This is 3 times the second term, that is , 3 * 6

Fourth term is is 54.

This is 3 times the third term, that is , 3 * 18

Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]

where n represents the position of the term in the sequence.

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I need help to solve this

Svetach [21]

Sorry, don't even think i've learned this yet, maybe look up a video from khan academy?

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3 years ago

Can anybody help me in this

Kobotan [32]

Answer:

a) I donot agree with him because as we see the sequence nicely we will find an interval of 8 between any two terms and 32 and 33 don't match them

Step-by-step explanation:

b) and c) Solution:

Given,

First term (a) = 4

Common difference (d) = 12-4 = 8

Now,

Since, they are in A.P.

nth term = a + (n-1)d

= 4 + 8(n-1)

= 4 + 8n-8

= 8n-4

Again,

1st method for c)

100th term = a + 99d = 4 + 99*8 = 4 + 792 = 796

200th term = a + 199d = 4 + 199*8 = 4 + 1592 = 1596

2nd method for c)

100th term = 8*100 - 4 = 800 - 4 = 796

200th term = 8*200 - 4 = 1600 - 4 = 1596

8 0

3 years ago

I need help with This question no links or I will report you

brilliants [131]

Answer:

Below.

Step-by-step explanation:

So let's do this Divide both sides.

equals to,

y+2>2

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2 years ago

Erica is making feathered caps for her school play. Each cap must have 3 feathers. Write an equation that represents the number

FrozenT [24]

Answer:

$f=3c$

Step-by-step explanation:

Given:

Number of feathers = $f$

Number of caps = $c$

Number of feathers in each cap = 3

Now, solving by setting up a proportion.

1 cap has 3 feathers. 'c' caps has 'f' feathers.

This gives,

$\dfrac{1}{3}=\dfrac{c}{f}$

Solving by cross multiplication, we get:

$1\times f=3\times c\\\\f=3c$

Therefore, the equation representing the number of feathers 'f' Erica needs to make 'c' caps is given as:

$f=3c$

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3 years ago

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Ierofanga [76]

Answer:

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Step-by-step explanation:

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3 years ago