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Reika [66]
3 years ago
9

In a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh

term is equal to 6. Find the sum of all ten terms.
Mathematics
1 answer:
poizon [28]3 years ago
4 0

Answer:

\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}

Step-by-step explanation:

We know that in a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh term is equal to 6. Therefore, we have

a_1+a_2=x\\a_3=x\\a_4=2x\\a_5=3x\\a_6=5x\\a_7=8x\\

We know that:

a_7=6\\\implies 8x=6\\x=\frac{3}{4}

We get:

a_1+a_2=x=\frac{3}{4}\\\\a_3=x=\frac{3}{4}\\\\a_4=2x=\frac{3}{2}\\\\a_5=3x=\frac{9}{4}\\\\a_6=5x=\frac{15}{4}\\\\a_7=8x=6\\\\a_8=13x=\frac{39}{4}\\\\a_9=21x=\frac{63}{4}\\\\a_{10}=34x=\frac{102}{4}\\

Therefore, we calculate

\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}

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Answer:

21 ft^2

Step-by-step explanation:

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area = b×h/2

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triangle 2 = (3×4)/2

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7 0
4 years ago
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3. The sum of the measures of a complement and a supplement of an angle is 200. What is the measure of the angle?
klasskru [66]
Hi there!

Let th' required angle = X

Then,

• Complement of th' angle = 90 - X
• Supplement of th' angle is = 180 - X

According to th' question,
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⇒ 2X = 70 

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5 0
3 years ago
The pet store has 8790 clownfish. they keep 6 fish in one tank . how many tanks do they have?
Gnoma [55]

Answer:

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Step-by-step explanation:

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Zanzabum

Answer:

x = 55° (nearest degree)

Step-by-step explanation:

Trig ratios:

sin(\theta)=\dfrac{O}{H} \ \ \ cos(\theta)=\dfrac{A}{H} \ \ \ tan(\theta)=\dfrac{O}{A} \ \ \

where \theta is the angle, O is the side opposite the angle, A is the side adjacent to the angle, and H is the hypotenuse of a right triangle

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2 years ago
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