Use the method of successive differences to determine the next term in the sequence.
-4, 18, 90, 264, 605, 1199, . . .
A)2143
B)2132
C)2174
D)2153

Question

Quizplus · Accepted Answer

The sequence of differences between consecutive terms is 14, 72, 174, 341, 594. The differences of these differences are 58, 102, 167, 253, which themselves have differences of 44, 65, 86. The next difference in this sequence is 107, leading to a next term difference of 594 + 107 = 701. Adding this to the last term 1199 gives 1900. Adding the next difference of 243 to 1900 gives 2143.

Use the Method of Successive Differences to Determine the Next