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数列   题数:53
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 an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?
240, 120, 60, 30, . . .In the sequence above, each term after the first is 1/2 of the preceding term. What is the least term of the sequence that is greater than 1 ?
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 set of numbers has the property that for any number t in the set, t + 2 is in the set. If –1 is in the set, which of the following must also be in the set? I. -3II. 1III. 5
In a certain sequence, the term xn is given by the formula xn = 2xn-1 - 1/2*(xn-2) for all n ≥ 2. If x0 = 3 and x1 = 2, what is the value of x3?
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (−1)k+1(12k ) ​. If T is the sum of the first 10 terms in the sequence, then T is
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?
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?
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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