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?
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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(52781) (Show Source):
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.
