Final answer:
The student is looking for the nth term of a non-arithmetic and non-geometric series starting with sn=2,7,15,24,38,... The pattern may potentially involve square numbers, and further analysis is required to determine the exact formula.
Step-by-step explanation:
The student is tasked with determining the explicit formula for the sequence that generates the given series sn=2,7,15,24,38,.... Observing the series, we can see that the difference between successive terms does not remain constant; hence, the series is not arithmetic. Similarly, the ratio of successive terms is not constant, indicating that the series is not geometric either. To look for a pattern, we can examine the differences between the terms more closely or look for other mathematical structures within the sequence.
If we consider the information given: n terms, we might hypothesize an underlying quadratic relationship since the series appears to involve square numbers. Analyzing the provided expressions and considering the pattern that emerges, we can deduce that this pattern may have to do with square numbers and operations on them, possibly leading to a formula involving n².
Further analysis would be required to establish an exact formula, which might involve fitting a polynomial to the series or examining the differences more systematically to obtain an nth term formula.