6.11. Show using the definition of increasing sequence provided on page 7 of the notes that the sequence an = n' - 6n2 -19n + 24 is increasing. As part of your work identify the value of N.Some sequences when far enough out in the sequence have terms that get larger, and others have terms that get smaller. We call these sequences monotonic Definition: Monotonic Sequence 1). A sequence is said to be increasing provided there is some positive integer N for which an N We see that aN an+1 for all n 2 N We see that an > an+1 > aN+2 >.. . We can see that this definition allows for the sequence to behave randomly initially but ultimately increase or ultimately decrease far enough out in the sequence. 3). Any sequence that is either ultimately increasing or decreasing in the above technical sense is called monotonic