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masya89 [10]
3 years ago
14

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 i

n the box. an=
Mathematics
1 answer:
Westkost [7]3 years ago
5 0

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

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