Define whether the sequences are arithmetic. If so, what is the recursive definition, and what is th

Jamison Estrada

Jamison Estrada

Answered question

2022-06-02

Define whether the sequences are arithmetic. If so, what is the recursive definition, and what is the next term in the sequences?
(a) 25 , 20 , 15 , 10 ,
(b) 2 , 4 , 7 , 12 , 13 ,

Answer & Explanation

Cesar Graham

Cesar Graham

Beginner2022-06-03Added 2 answers

(a) 25 , 20 , 15 , 10 ,
The sequence is arithmetic

a 1 = 25
a 2 = 20
a 3 = 15
a 4 = 10
We can see the common difference d = 5
Thus, the next term will be a 5 = 5

Here, recursive definition is
a n = a 1 + ( n 1 ) ( 5 ) = a 1 5 ( n 1 )

(b) 2 , 4 , 7 , 12 , 13 ,

a 1 = 2
a 2 a 1 = 4 2 = 2
a 3 a 2 = 7 4 = 3
a 4 a 3 = 12 7 = 5
a 5 a 4 = 13 12 = 1
Difference between any two consecutive terms is not same, thus, the sequence is not arithmetic.

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