. Choos e the n ext term in the s eque nce 2,5,11,20,32

To find the next term in the sequence, we need to identify the pattern or rule that the sequence follows. Let's examine the differences between consecutive terms:1. Difference between the second term and the first term: 2. Difference between the third term and the second term: 3. Difference between the fourth term and the third term: 4. Difference between the fifth term and the fourth term: We can observe that the differences between consecutive terms are increasing by 3 each time. This suggests that the sequence follows a quadratic pattern. To find the next term, we need to determine the formula for the nth term of the sequence.Let's assume the sequence follows a quadratic formula of the form , where , , and are constants.Using the first three terms of the sequence, we can set up a system of equations:For :\(a(1)^2 + b(1) + c = 2\) For :\(a(2)^2 + b(2) + c = 5\) For :\(a(3)^2 + b(3) + c = 11\) Solving this system of equations, we find that , , and . Therefore, the formula for the nth term of the sequence is .To find the next term in the sequence, we substitute into the formula: Therefore, the next term in the sequence is 40.