Answer:
55 and 91 are not prime.
Step-by-step explanation:
[tex]12(1) -5=7\\12(2) -5=19\\12(3) -5=31\\ 12(4) -5=43\\12(5) -5=55\\12(6) -5=67\\12(7) -5=79\\12(8) -5=91\\12(9) -5=103[/tex]
The two digits numbers in the sequence that are not prime: 55 and 91
"It is a list of numbers in particular order."
"A natural number that are divisible by only 1 and the number itself."
For given example,
The nth term of a sequence is 12n -5.
The numbers in the sequence that have two digits and are not prime.
The two digit numbers have range: [10, 99]
Assuming n be a positive natural number,
⇒ 10 ≤ 12n - 5 ≤ 99
⇒ 10 + 5 ≤ 12n - 5 + 5 ≤ 99 + 5
⇒ 15 ≤ 12n ≤ 104
⇒ 15/12 ≤ 12n/12 ≤ 104/12
⇒ 1.25 ≤ n ≤ 8.67
This means, 'n' can take values 2, 3, 4, 5, 6, 7, and 8
For n = 2,
12n -5
= 12(2) - 5
= 19 which is a prime number.
For n = 3,
12n -5
= 12(3) - 5
= 31 which is a prime number.
For n = 4,
⇒ 12n -5
= 12(4) - 5
= 43 which is a prime number.
For n = 5,
⇒ 12n -5
= 12(5) - 5
= 55 which is not prime.
For n = 6,
⇒ 12n -5
= 12(6) - 5
= 67 which is a prime number.
For n = 7,
⇒ 12n -5
= 12(7) - 5
= 79 which is a prime number.
For n = 8,
⇒ 12n -5
= 12(8) - 5
= 91 which is not prime.
From above, the two digits numbers in the sequence that are not prime: 55 and 91
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