给定公比为 q （ q≠1）的等比数列{ a n}，设 b 1=a 1+a 2+a 3，b 2=a 4+a 5+a 6，…，b n=a 3n-2+a 3n-1+a 3n，…，则数列{ b n}（ ）
A．是等差数列
B．是公比为 q 的等比数列
C．是公比为 q 3的等比数列
D．既非等差数列也非等比数列
解析：由题意an=a1qn-1，bn=a 3n-2+a 3n-1+a 3n
∴
=bn+1 bn
=a3n+1+a3n+2+a3n+3 a3n-2+a3n-1+a3n a1q3n+a1q3n+1+a1q3n+2 a1q3n-3+a1q3n-2+a1q3n-1
=
=q3a1q3n(1+q+q2) a1q3n-3(1+q+q2)
因此，数列{bn}是公比为q3的等比数列．
故选C．
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have more bananas, apples, oranges, tomatoes and lettuce (莴苣) because fruits and vegetables are good for (对……有好处，益处) you. But don't eat too much chocolate. It's not good healthy food. Healthy food can make you grow and make you strong and happy. Remember there is a saying (谚语，俗语), " An apple a day keeps the doctor away." Sports can also keep you healthy. Get up early and do some sports every day. Don't be lazy (懒惰的)! You will be healthy and happy. ( ) 1. Bananas are healthy food. ( ) 2. Chocolate is a kind of fruit. ( ) 3. Chocolate can make you grow well. ( ) 4. " An apple a day keeps the doctor away." means apples are very good. ( ) 5. Sports are also very important to help keep you healthy. |