Find a formula for the general term of the sequence 4 2 , − 5 4 , 6 8 , − 7 16 , 8 32 , assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 4 2 a2 = − 5 4 a3 = 6 8 a4 = − 7 16 a5 = 8 32 . Notice that the numerators of these fractions start with 4 and increase by whenever we go to the next term. The second term has numerator 5, the third term has numerator 6; in general, the nth term will have numerator . The denominators are powers of , so an has denominator . The signs of the terms are alternately positive and negative so we need to multiply by a power of −1. Here we want to start with a positive term and so we use (−1)n − 1 or (−1)n + 1. Therefore, an = (−1)n − 1 · .