For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?
In the infinite sequence a1, a2, a3, . . . , an, . . . , each term after the first is equal to twice the previous term. If a5 - a2 = 12, what is the value of a1 ?
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?
p, r, s, t, uAn arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of letters shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?I. 2p, 2r, 2s, 2t, 2uII. p–3, r–3, s–3, t–3, u–3III. p2, r2, s2, t2, u2
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