Question

It is given that the general term of a sequence is T_n = log_2 r^{n − 10}, where r is a constant and 0 < r < 1.

Show that the sequence is an arithmetic sequence, and find the common difference.

If T_k < sT_{k − 1}, where s > 2, can the value of k be greater than 11? Explain your answer.

Take r = 0.5. Let a, b, c be three consecutive terms of the sequence, where a > b > c and a≠ 0. Does the graph of y = ax^2 + 3bx + c intersect the x-axis at two distinct points? Explain your answer.

Steven Zheng posted 2 months ago

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