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kherson [118]
3 years ago
11

What is the explict rule for the sequence 12,22,32,42​

Mathematics
1 answer:
icang [17]3 years ago
8 0

The explicit rule for given sequence is:

a_n=2+10n

Further explanation:

We have to determine first of all if the sequence is arithmetic or geometric.

  • If the difference of two consecutive terms is same then the sequence is arithmetic sequence
  • If the ratio of two consecutive terms is same then the sequence is geometric sequence

Given sequence is:

12,22,32,42​

a_1=12\\a_2=22\\a_3=32\\.......\\Let\\d=Common\ difference\\d=a_2-a_1=22-12=10\\d=a_3-a_2=32-22=10

The common difference is 10 which is same for all consecutive terms. So the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference

Putting the values of a1 and d

a_n= 12+(n-1)(10)\\a_n=12+10n-10\\a_n=2+10n

The explicit rule for given sequence is:

a_n=2+10n

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

  • brainly.com/question/1522572
  • brainly.com/question/2491745

#LearnwithBrainly

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Enter a problem...

Algebra Examples

Popular Problems Algebra Solve by Substitution 3x-4y=9 , -3x+2y=9

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3

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3

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+

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.

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x

=

3

+

4

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3

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2

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18

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−

2

and simplify.

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x

=

3

+

4

y

3

y

=

−

9

Replace all occurrences of

y

in

x

=

3

+

4

y

3

with

−

9

.

x

=

3

+

4

(

−

9

)

3

y

=

−

9

Simplify

3

+

4

(

−

9

)

3

.

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x

=

−

9

y

=

−

9

The solution to the system of equations can be represented as a point.

(

−

9

,

−

9

)

The result can be shown in multiple forms.

Point Form:

(

−

9

,

−

9

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Equation Form:

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image of graph

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:
*****************************
Our sequence is
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:
The third integer is 86
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