1. The problem asks to find the next term in the sequence (16): 7, 14, 23, 34, 47, ... 2. Let's analyze the differences between consecutive terms: $$14 - 7 = 7$$ $$23 - 14 = 9$$ $$34 - 23 = 11$$ $$47 - 34 = 13$$ 3. The differences are increasing by 2 each time: 7, 9, 11, 13, ... 4. The next difference should be $$13 + 2 = 15$$ 5. Add this difference to the last term to find the next term: $$47 + 15 = 62$$ 6. Therefore, the next term in the sequence is **62**. This method uses the concept of arithmetic progression in the differences between terms, which is common in quadratic sequences.