Anet said that the common difference in the sequence below is -2. Is she correct? Justify your answer using complete sentences a
nd proper grammar. 1, -2, 4, -8....
A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n - 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar.
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The given sequence is 1, -2, 4, -8, ...., Multiply the 1st term by -2 to obtain 1*(-2) = -2 (the 2nd term) Multiply the 2nd term by -2 to obtain -2*(-2) = 4 (the 3rd term) Multiply the 3rd term by -2 to obtain -2*(4) = -8 (the 4th term) Answer: Anet is incorrect. This is a geometric sequence with a common ratio of -2.
Initial size = 24 (This is the 1st term in the sequence) 2nd term = 24 +5 = 24 + (2-1)*5 3rd term = 24 + 5 + 5 = 24 +(3-1)*5 By induction, the n-th term is A(n) = 24 + (n-1)*5 Answer: The given formula is correct.
