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State weather each sequence is arthmetic and justify your answer. If the sequence is artithmetic write a recursive and an explicit formula to represent it. 52, 40, 28, 16

Answer :

absor201

The sequence is an arithmetic sequence.

The explicit formula for the given sequence is: a_n = 64-12n

Further explanation:

In order to find if the given sequence is arithmetic or not, the common difference has to be checked. The common difference the the difference between two consecutive terms of an arithmetic sequence.

So,

40-52 = -12

28-40 = -12

16-28 = -12

The common difference is same i.e. d = -12 so the given sequence is arithmetic sequence.

Explicit formula for Arithmetic Sequence:

The general formula for arithmetic sequence is:

[tex]a_n=a_1+(n-1)d\\Here\\a_n\ is\ nth\ term\\a_1\ is\ the\ first\ term\\and\ d\ is\ common\ difference\\[/tex]

As we know

a_1 = 52

and

d = -12

Putting the values in general formula for arithmetic sequence

[tex]a_n = a_1+(n-1)d\\a_n = 52+(n-1)(-12)\\a_n = 52-12n+12\\a_n = 64-12n[/tex]

Keywords: Arithmetic Sequence, Recursive Formula

Learn more about arithmetic sequence at:

  • brainly.com/question/1522572
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