Anet said that the common difference in the sequence below is -2. is she correct? justify your answer using complete sentences and proper grammar.
1, -2, 4, -

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)

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

The given formula is correct.