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2 years ago

PLEASE HELP!! Find the sixth term of the sequence 14,9,4,..

Mathematics

1 answer:

jeka942 years ago

8 0

Answer:

Step-by-step explanation:

We notice this is an arithmetic sequence.

14, 9, 4.

common difference = d = 14 - 9 = 5

first term a_1 = 14

Find 6th term a_6

a_n = (n -1)*d + a_1

a_6 = (6 -1)*5 + 14

a_6 = 5*5 + 14 = 25 + 14 = 39

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Let x as the missing segment.

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According to the Thales theorem :

$\frac{26}{x} = \frac{12}{36} \\$

$\frac{26}{x} = \frac{12}{12 \times 3} \\$

$\frac{26}{x} = \frac{1}{3} \\$

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$\frac{x}{26} = \frac{3}{1} \\$

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Multiply sides by 26

$26 \times \frac{x}{26} = 26 \times 3 \\$

$x = 26 \times 3$

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