This sequence is generated by the formula (a_n = n^3 + n^2) with n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1³+1² = 2, 2³+2² = 12, 3³+3² = 36, 4³+4² = 80 and 5³+5² = 150. For n = 6 the formula gives 6³+6² = 216+36 = 252. Thus 252 maintains a single algebraic rule that explains all the terms.
Option A:
Option A, 252, matches exactly the value obtained by substituting n = 6 into the rule (a_n = n^3+n^2). Since this rule already accounts for every earlier term, extending it to 252 keeps the series perfectly consistent. Hence 252 is the correct continuation.
Option B:
Option B, 254, cannot be expressed as 6³+6² and does not result from the same expression for any natural n in order. Using 254 would break the clean connection between term position and value. Therefore it is not the right answer.
Option C:
Option C, 256, is numerically close but again does not obey the formula (n^3+n^2). It has no direct link to the pattern that generates the given sequence and so is not acceptable.
Option D:
Option D, 258, deviates even further from the predicted value and similarly lacks a basis in the generating rule. Selecting 258 would force an ad hoc change in the pattern, making it incorrect as the next term.
Comment Your Answer
Please login to comment your answer.
Sign In
Sign Up
Answers commented by others
No answers commented yet. Be the first to comment!