SOLUTION: The sequence 2, -4, a , and b is such that the first three terms form an arithmetic sequence and the last three terms form a geometric sequence. What is the values of a and b?

Question 1191254: The sequence 2, -4, a , and b is such that the first three terms form an arithmetic sequence and the last three terms form a geometric sequence. What is the values of a and b?
Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
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Then the common difference is  -4 - 2 = -6;


therefore, a = -4 -6 = -10  as the next term of the arithmetic progression;


hence,  the common ratio is   = 2.5;


It implies that b = 2.5*(-10) = -25 as the next term of the geometric progression.


ANSWER.  a= -6;  b= -25.

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