Mathematics
Mathematics, 08.04.2020 00:24, pineapplepizaaaaa

Find a formula for the general term of the sequence 4 2 , βˆ’ 5 4 , 6 8 , βˆ’ 7 16 , 8 32 , assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 4 2 a2 = βˆ’ 5 4 a3 = 6 8 a4 = βˆ’ 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 βˆ’1. Here we want to start with a positive term and so we use (βˆ’1)n βˆ’ 1 or (βˆ’1)n + 1. Therefore, an = (βˆ’1)n βˆ’ 1 Β· .

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Find a formula for the general term of the sequence 4 2 , βˆ’ 5 4 , 6 8 , βˆ’ 7 16 , 8 32 , assuming tha...

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