算数-数列

flyfish 2015-11-16

等差数列（arithmetic sequence）：如果一个数列从第二项起，每一项与它的前一项的差等于同一个常

数。这个常数叫做等差数列的公差（common difference）。

等比数列（geometric sequence）：如果一个数列从第二项起，每一项与它的前一项的商等于同一个常数。这个常数叫做等比数列的公比（common ratio）

一

The first term of a sequence of numbers is 1. If each term after the first is the product of -2 and the preceding term，what is the sixth term of the sequence？

preceding是在前面的意思。本数列中第一项后的每一项，是-2和前一项的乘积，故这是一个公比为-2的等比数列。

二

1，4，10，t，46，…

In the sequence above，the first term is 1 and each term after the first is 2 more than twice the previous term. What is the value of t？

后一项比前一项的2倍还多2

三

5，a，b，5，…

In the sequence above，the first term is 5 and the second term is a. Each term

after the second is the product of the two immediately preceding terms. If a＜0，what is

the 10th term of the sequence？

521

第二项后的每一项都是它前面2项的乘积

四

Each term of a certain sequence is greater than the term

before it. The difference between any two consecutive terms in the sequence is always the

same number. If the third and sixth terms of the sequence are 17and 77，respectively，what

is the eighth term？

consecutive表示连续的意思。由题意，本题中的数列后一项总比前一项大，且连续2项的差是一个常数，故这是一个等差数列。

五

In a sequence，each term after the first is found by adding the constant k to the

preceding term. The 10th term in the sequence is 23，and the 16th term is 41. What is the

7th in the sequence？

14

这是一个公差为k的等差数列