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A recursive rule for an arithmetic sequence is a1=4;an=an−1−3 . What is the explicit rule for this sequence? Enter your answer in the box. an=

User David Gill
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Answer:

The explicit rule for the arithmetic sequence is given by:


a_n = a_1+(n-1)d ......[1]

where,


a_1
is the first term

n is the number of terms and

d is the common difference for two consecutive terms.

As per the statement:

A recursive rule for an arithmetic sequence is:


a_1 = 4


a_n = a_(n-1)-3

The recursive formula for the arithmetic sequence is given by:


a_n = a_(n-1)+d

then;

On comparing we get;

d = -3

Substitute the given values in [1] we have;


a_n = 4+(n-1)(-3)


a_n = 4 -3n+3 = 7-3n

Therefore, the explicit rule for this sequence is,
a_n = 7 -3n

User Marieanne
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