Aset is under an operation (such as addition, etc) if any two elements of that set always generate another element in the set, when the operation is performed on them.

If any two elements of the set always generate another element in the set itself, when an operation is performed on them, then that property is called CLOSURE.

Also, that set is said to be CLOSED under that operation.

Hence, the correct answer to fill the blank is CLOSED.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.