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Nikolay [14]
3 years ago
12

Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of

the second fourth and fifth
Mathematics
1 answer:
bogdanovich [222]3 years ago
6 0

Answer:

see below

Step-by-step explanation:

We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.

x + 5x + 10 = 3(3x + 8) - 41

6x + 10 = 9x + 24 - 41

6x + 10 = 9x - 17

3x = 27

x = 9

The numbers are 9, 10, 11, 12, 13.

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A geometric sequence is defined by the equation an = (3)3 − n.
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PART A

The geometric sequence is defined by the equation

a_{n}=3^{3-n}

To find the first three terms, we put n=1,2,3

When n=1,

a_{1}=3^{3-1}

a_{1}=3^{2}

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When n=2,

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When n=3

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The first three terms are,

9,3,1

PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
r= \frac{a_{2}}{a_{1}}
r = \frac{3}{9}

r = \frac{1}{3}

PART C

To find
a_{11}

We substitute n=11 into the equation of the geometric sequence.

a_{11} = {3}^{3 - 11}

This implies that,

a_{11} = {3}^{ - 8}

a_{11} = \frac{1}{ {3}^{8} }

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PLZZZZZZZZZZZZZZZZ HELP IM IN A RUSH
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B .....................
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Read 2 more answers
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