A) The given sequence is decreasing by 7 each time. Therefore, the next term would be 1 less than 8, or 7.
B) The given sequence is increasing by successive odd integers, starting with 3. To find the nth term of this sequence, we can use the formula:
nth term = first term + (n-1) * common difference
The first term of this sequence is 4, and the common difference is the successive odd integers. The difference between each term and the previous term is 3, 5, 7, 9, and so on. So, the common difference is 2 more than the index of the term.
For example, the second term (n=2) is 7, which is 3 more than the first term. Therefore, the common difference is 3. The third term (n=3) is 12, which is 5 more than the second term. Therefore, the common difference is 5-3=2.
Thus, we can write the nth term as:
nth term = 4 + (n-1) * (n+1)/2
For example, the fourth term (n=4) would be:
nth term = 4 + (4-1) * 5/2 = 4 + 3*5/2 = 4 + 15/2 = 11.5
Therefore, the nth term of the sequence is 4 + (n-1) * (n+1)/2.