Question

Consider the sequence 0, 4, 9, 15, 22. Find the explicit formula for the nth term.

a) n²
b) n² + 2
c) n(n + 1)/2
d) n(n + 2)/2

Answer 1

The explicit formula for the nth term of the given sequence 0, 4, 9, 15, 22 is n² + 2n. By analyzing the differences between the terms, we can deduce that the formula for the nth term is n². Additionally, each term is 2 greater than the perfect square corresponding to the term number, so we add 2n to the perfect square formula.

Step-by-step explanation:

The explicit formula for the nth term of the given sequence 0, 4, 9, 15, 22 is n² + 2n. We can find the explicit formula by observing the pattern in the sequence. The difference between each term and its preceding term progressively increases by 1, which suggests a quadratic relationship. By analyzing the differences, we can deduce that the formula for the nth term is n². However, there is an additional pattern where each term is also 2 greater than the perfect square corresponding to the term number. So, we add 2n to the perfect square formula to get the explicit formula as n² + 2n.