Question

The n-th term of a number pattern is as follows:

Tn = 7n + 6 if n is a prime number and Tn = n²-8 if n is not a prime number
Determine the value of T9 - T7​

Answer 1

9 = 3² is not prime, so $T_9 = 9^2-8 = 81-8 = 73$.

7 is prime, so $T_7 = 7\times7+6 = 55$.

Then the difference is $T_9 - T_7 = 73 - 55 = \boxed{18}$.