Final answer:
The explicit formula for the given sequence is an = (-1)n+1 * (n-1)/n, where n represents the term number in the sequence, and this formula captures the alternating signs and the pattern in the numerators and denominators.
Step-by-step explanation:
The given sequence is 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, and we need to find an explicit formula for this sequence. Observing the pattern, we can deduce that the n-th term, an, is given by (-1)n+1 multiplied by (n-1)/n. This sequence alternatively changes signs between positive and negative with increasing natural numbers in the numerator and consecutive natural numbers in the denominator.
To construct the formula step by step, first note the sign of the terms. They alternate beginning with a positive term. The exponent (-1)n+1 will control the sign alternating for each term. Next, observe the numerator is always one less than the place in the sequence; thus, the numerator is (n-1). Finally, the denominator is the same as the place in the sequence, which means it is n. Therefore, putting it all together, we get an = (-1)n+1 * (n-1)/n.