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3 years ago

The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a(n)=6

Mathematics

1 answer:

Aleks04 [339]3 years ago

8 0

Answer:

Step-by-step explanation:

Given the nth term of an arithmetic sequence to be Tn = a+(n-1)d

a = first term of the sequence

n = number of terms

d = common difference.

Given the first element a = 2 and 22nd to be 14

T22 = a+(22-1)d = 14

a+21d = 14

Substtuting a = 2 into the equation to get d

2+21d = 14

21d = 12

d = 12/21

d = 4/7

The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

Tn = 2+(n-1)4/7

Given Tn = 6

6 = 2+(n-1)4/7

6 = 2+4/7 n - 4/7

6-2+4/7 = 4/7 n

32/7=4/7 n

32 = 4n

n = 32/4

n = 8

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Help me out please and thank you

faust18 [17]

<h3>Answer: 1</h3>

========================================================

Explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

$d = \text{Distance from B to C}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y^2)^2}\\\\d = \sqrt{(-2-(-3))^2+(-1-(-2))^2}\\\\d = \sqrt{(-2+3)^2+(-1+2)^2}\\\\d = \sqrt{(1)^2+(1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\$

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

$A = \text{Area of triangle}\\\\A = \frac{1}{2}*\text{Base}*\text{Height}\\\\A = \frac{1}{2}*\sqrt{2}*\sqrt{2}\\\\A = \frac{1}{2}*\sqrt{2*2}\\\\A = \frac{1}{2}*\sqrt{4}\\\\A = \frac{1}{2}*2\\\\A = 1\\\\$

The area of the triangle is 1 square unit.

See diagram below.

5 0

3 years ago

SAM IS painting her sisters wall. The wall has 2 windows. It has a base 0f 100 and a height of 200. What is the area of the wall

juin [17]

Answer:

200 x 100 = 2000, he might not

Step-by-step explanation:

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3 years ago

Angelina is making flower bouquets. She has 24 tulips and 36 roses. She wants all the bouquets to be identical, containing the s

Lemur [1.5K]

Answer:

Therefore the maximum number of bouquets is 12.

Step-by-step explanation:

Given that, Angelina has 24 tulip and 36 roses.

To find the number bouquets, we need the find out the g.c.d (greatest common divisor) of 24 and 36.

24= 2×2×2×3

36=2×2×3×3

The common factors are = 2,2,3

The g.c.d of 24 and 36 is =2×2×3

= 12

Therefore the maximum number of bouquets is 12.

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4 years ago

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sammy [17]

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3 years ago

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sesenic [268]

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Let's find the height (BA)
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7 0

3 years ago