For the sequence 96, 48, 24, 12, 6, write an explicit formula.
Answer (2)
a 1 = 96 ; a 2 = 48 ; a 3 = 24 ; a 4 = 12 ; a 5 = 6 a 1 = a 2 : 2 → 96 : 2 = 48 a 2 = a 3 : 2 → 48 : 2 = 24 a 3 = a 2 : 2 → 24 : 2 = 12 a 4 = a 3 : 2 → 12 : 2 = 6 t h ere f ore a n = 96 : 2 n − 1 = 2 n − 1 96 c h ec k : a 1 = 2 1 − 1 96 = 1 0 96 = 96 a 2 = 2 2 − 1 96 = 2 1 96 = 2 96 = 48 a 3 = 2 3 − 1 96 = 2 2 96 = 4 96 = 24 ⋮
The explicit formula for the sequence 96, 48, 24, 12, 6 is a n = 2 ( n − 1 ) 96 . This formula can be derived by recognizing the pattern of each term being half of the previous term. The formula was verified by substituting the term numbers back into it to confirm the results match the original sequence.
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