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2 years ago

The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187. Calculate the 21st term of the sequence.

Mathematics

1 answer:

Gnesinka [82]2 years ago

3 0

Answer:

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

The sum of n terms of an arithmetic sequence is ...

Sn = (2·a1 +d(n -1))(n/2)

Using these relations and the given values of a11 and s11, we can find a1 and d:

a11 = a1 +d(11 -1) = 32

S11 = (2·a1 +d(11 -1))(11/2) = 187

These simplify to ...

a1 +10d = 32

2a1 +10d = 34 . . . . multiply the second equation by 2/11

Subtracting the first of these from the second, we get ...

a1 = 2

Then the common difference is ...

d = (32 -2)10 = 3

And the 21st term is ...

a21 = 2 +3(21 -1) = 62

The 21st term is 62.

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Art [367]

Answer:

x=4, y=4

Step-by-step explanation:

X=(4+8y)/9

-6×(4+8y)/9 +6y=0

-2×(4+8y)/3+ 6y=0

-2×(4+8y) + 18y =0

-8-16y+18y=0

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-6x+6×4=0

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2 years ago

15x+12(10-x)=141 make sure to use steps to solve!

goldfiish [28.3K]

Answer: x=7

Step-by-step explanation: First you distribute the 12 to (10-x). That then gives you 15x+120-12x=141. Now you combine like terms. So you do 15x-12x=3x. Your new equation now is 3x+120=141. Subtract 120 from 141 and mark it out. That leaves you with 3x=21. Divide both sides by 3. Your final answer is x=7.

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2 years ago

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natulia [17]

0.000000000224 i think thats the answer could be wrong

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3 years ago

Write eachfraction units simplest form. 18/4= ____. 24/32=_______

disa [49]

Answer:18/4= 9/2

24/32= 3/4

Step-by-step explanation:

for 18/4 divide both numbers by 2

= 9/2

for 24/32 divide both numbers by 8

=3/4

5 0

3 years ago

Read 2 more answers

A parabola with the vertex at (1.5, 12.5) inscribes a segment of length 5 on x-axis. What is the area of the triangle formed by

damaskus [11]

Answer:

20 units²

Step-by-step explanation:

The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at

1.5 ± 5/2 = {-1, 4}

Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...

0 = a(4 -1.5)² +12.5

0 = 6.25a +12.5 . . . . . simplify

0 = a +2 . . . . . . . . . . . divide by 6.25

-2 = a

Then the standard-form equation of the parabola is ...

y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5

y = -2x² +6x +8

This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...

A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²

5 0

2 years ago