例1. 1,-2,-3,-2,1,( ) a.6 b.3 c.-1 d.-4 例2. 2.1,5.2,8.4,11.8,14.16,( ) a.19.52 b.19.24 c.17.82 d.17.32 例3. 1,-5,10,10,40,( ) a.-35 b.50 c.135 d.280 例4. 27, 11, 16, 5, 11, 6, ( ) a.5 b.9 c.13 d.17 例5. 152, 178, 226, 320, 532, ( ) a.1078 b.1727 c.1072 d.1071 [答案解析] 例1. [答案]a 数列无明显特征,优先考虑做差.做差后得到新数列:-3,-1,1,3,( ),为公差是2的等差数列,新数列中下一项=3 2=5,则所求项=1 5=6. 例2. [答案]d 解析:数列为小数数列,做差无规律,考虑小数点前后的机械划分.划分为: 整数部分:2,5,8,11,14,( ),为公差是3的等差数列,下一项为17; 小数部分:1,2,4,8,16,( ),为公比是2的等比数列,下一项为32. 综上可得:所求项为17.32. 例3. [答案]d 解析: 数列存在明显的倍数关系,优先考虑做商.做商后得到新数列:-5,-2,1,4,( ),为公差是3的等差数列,新数列下一项=4 3=7,则所求项=40×7=280. 例4. [答案]a.解析:每一项等于前两项之差的绝对值,下一项为|11-6|=(5). 例5. [答案]a.解析:多级等差数列变式.做三次差变为等比数列.