what is the 8th term of -5,2,21,58
The change from one number to the next is 7, 19, 37. These are prime numbers.
If you write out the list of prime numbers, you find that from 7 to 19 is 3 steps;
from 19 to 37 is 4 steps. Continuing this progression, 5 steps beyond 37 is 59.
We add 59 to 58 to arrive at 117. Back to the primes: 6 steps beyond 59 is 83.
Add 83 to 117 to get 200. Next, 7 steps beyong 83 is 113. Add 113 to 200, 313.
One more time: 8 steps beyond 113 is 163. Add 163 to 313 and we have 476,
the eighth term in our sequence.