In here, the first term is -17, the second is -13 and the third is -9. Note that if we subtract the second and the first term we get -13 - (-17 ) = 17-13 = 4. The same happens if we subtract the third term and the second (-9 -(-13) = 13 - 9 = 4). This means that we can obtain the next term by simply adding 4 to the previous term. Consider the first term -17. The second one would be -17 + 4. The third term would be -17 + 4 + 4 = -17 + 2*4.
Note that if we wanted the third (3) term, then we subtract 1 to the number of the term (3-1 = 2), then multiply this number by 4 and finally add it to the first term (-17).
So, to calculate the 4th term, we proceed as follows:
1. 4- 1 = 3
2. 3*4 = 12
3. -17 + 12 = -5
So the 4th term would be -5. Note that is the same as taking the previous one (-9) and adding 4 (-9 +4 = -5). So this shows that our procedure is correct.
So, to find the nth term, we follow the formula
This formula corresponds to putting all the previous steps together all at once. Since we are looking for the 12th term, we make n = 12. So we replace this value into the formula
So the 12th term of the sequence is 27