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prisoha [69]
3 years ago
11

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Mathematics
1 answer:
Sati [7]3 years ago
6 0

Answer:

              a₁ = -5, d = 7,  a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:    \boxed{\bold{a_n=7n-12}}

Step-by-step explanation:

a₁ + a₂ + a₃ = 6    

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2     ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7   ⇒  a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}

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The answer is C. 1

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3 years ago
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The 100th term in 8, 13, 18,23, 28,...
Lunna [17]

Answer:

The 100th term of the sequence is 503.

Step-by-step explanation:

Given : Sequence 8, 13, 18,23, 28,...

To find : The 100th term in the sequence ?

Solution :

Sequence 8, 13, 18,23, 28,... is the arithmetic sequence

Where, First term is a=8

The common difference is d=13-8=5

The nth term of the sequence is given by a_n=a+(n-1)d

The 100th term is given by,

a_{100}=8+(100-1)5

a_{100}=8+(99)5

a_{100}=8+495

a_{100}=503

The 100th term of the sequence is 503.

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3 years ago
How much interest is earned on a $5,000 loan at 10% interest for 3 years?
Aleksandr-060686 [28]

Answer:

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3 years ago
Solve the system of elimination -2x+2y+3z=0 -2x-y+z=-3 2x+3y+3z=5
Dahasolnce [82]

Answer:

x = 1 , y = 1 and z = 0

Step-by-step explanation:

-2x+2y+3z=0    ------(1)

-2x-y+z=-3     --------(2)

2x+3y+3z=5    ---------(3)

<u>To find the values of x,y and z</u>

(3) - (2)⇒ 2y + 4z = 2

y + 2z = 1   --------(4)

(1) - (2)⇒ 3y +2z =3   ---(5)

(5) - (4)⇒ 2y = 2

y = 1

Substituting the value of y in (4) we get z =0

Substituting the value of y and z  in (1) we get x = 1

Therefore x = 1 , y = 1 and z = 0

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3 years ago
An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?
IgorC [24]
Assuming 0 and 100 are included in the possible choices:

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8 0
3 years ago
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