2021版数学攻略大一轮复习 6.3 等比数列(试题部分)

年考情考点 内容解读

预测热度

数列的

考题示例

考向

关联考点

有关概念及运

n

n

★★★

性质及

★★★

.,,.

n

,

,,.,.

考点一 等比数列的有关概念及运算

{a},

=

q= +a++a=

{a},

=

q= +a++a= .

{a}

=

n+1 n+2 A

{a},

= . 考点二 等比数列的性质及应用

,

,

m+n=p+q,{a},m=apq{a} A. B. B

,

c= . {a},

+5

q

,

q= .

{a}

+a A. B. A

{a}

n+1=2,𝑎 .𝑎

,,,,,,.

,, .

=p-2,

=a

=a

+a

=a

+a

+a

{a}

n

=p-2,

n★*.

p

{a};{𝑎𝑛}},.

{a},

q=𝑎=,𝑎𝑎

𝑎𝑎𝑛+1=

=,𝑎2𝑛𝑎𝑛+1=

=,𝑎2𝑛{𝑎𝑛

}

=a

+a

++a

,

,{a}

=aq=2★*

:{𝑎𝑛},}:𝑎𝑛=4, 2-𝑛3-𝑛

=n×2,}

,}

=,

,

=,

,

=

𝑎𝑛{a}

,

𝜆

,

{a}

n

=1+,

{a},; 1-𝜆

=1+n+1=1+n+1

n+1=n+1,

n+1.

𝑎𝑛+1=

𝜆

.𝜆-11-𝜆 𝜆-1

=

(

𝜆

)

𝑛-1

=1-(

𝜆

)

.

=

(

𝜆

)

=,(

𝜆

)

=

,n+1

n+1

,,𝜆-15 5 𝜆-1 𝜆-1

n+1

n+1

,

A

考点一 等比数列的有关概念及运算

{a}}

=b=b𝑎= .𝑏

{a}}

=b+ab=a.{a};+b+b++b. ,..

b+b+b++b=1+3+3++3=

b+b+b++b=1+3+3++3=

.{a}n.=,=

.

+a

}

bb=a,

bqbq

q

b=bq=3.𝑛

,,.,.考点二 等比数列的性质及应用 ,

.

,,,. A.

B.

5 7 B

考点一 等比数列的有关概念及运算

:,,,:,

,

B

5

{a}

n

.

=,𝑎=a,

=

.

{a}

{a}

n+1.

b=

𝑛.𝑎=.n+1 𝑛+1 =𝑎 2𝑎𝑛,

bn+1=2b,

𝑛=2,

=n.𝑎

,

=

.

{a}

+a

= . 𝑛

b;},;{a}.

𝑛

n=1

=4a,

n=2

=3a,

b}

.𝑛+1 𝑛

b}

.𝑛

{a}=4a.{a};

{a}

n

.

m

.{a}

=q.

q=4q,

q=-2

=2.𝑛

m=63

m.

=2,

=2

m=63

m

,,,. :.

q

,.....n.n.

{a}

n

,}

n

T+b

+b};

T

. .{a}

}

=q.

+b=2

d+q=3.

+b=5

2d+q𝑑

𝑑

𝑞

),𝑞

}

b=2.

b=21

q

q=-5

q=-5,

q=4

,

考点二 等比数列的性质及应用

{a}

=3a+4a,

,

a=5+2,

b= . {a}+a{a}n .

{a}=2a{a};

b,}

n

.

{a

{a}

,

n

.

=

=

, .{a}

q

{a}

=2×4=2.

b}

n

1+3++2n-1=n.

{a}

+a+a

+a+a B

{a}{lg}

{a}

q

.q>1{a} A. B.

,

+a+a+a+a+a).

<a<a >a<a<a>a >a>a B = .

{a},

+a=2e,

+= .

{a}

,

n

.

,

.

{a}

+a+a

q= ;

n

= . n+1

{a}

n

.

{a};

,

n+1n+2. .{a}

𝑎

𝑎𝑞

{a}.

=𝑎(1-𝑞

=-

n+2n+1=-

1-𝑞

𝑛+3𝑛+2

𝑛

𝑛+1

.=2[-

=2[-

𝑛

𝑛+1

],.

=a

n

:S.

=a

n

:S

=(𝑎+𝑎𝑛=na

+𝑛(𝑛-1)

=a

q.

n

:S

=𝑎

(1-𝑞𝑛 ::n+1 ::𝑎𝑛+1=q(q.𝑎𝑛 𝑛𝑎

1-𝑞

,:𝑎+𝑐=b

c=b.

,

bd

,2𝑎+𝑏 2𝑐+𝑑 B.

B

{a}

d

,

.

,

,

,

{a}<a<a A. B.

{a}

,

n

.

{a}

,

n

.

=

,

𝑎

𝑎

𝑛+1

n+1=3n+1=3(1-3

=.

,n+1=3n+1=,+3=𝑛+1

,

{a}{a}

n

= . = = . ;

{a}

+a+a

.

{a},

n+1=2.

q

;{a}

n

,n+1.𝑎

-𝑎

𝑎-𝑎

{a},𝑎

-𝑎

=aq-a

=3.,

n+1=3n+1=2,{a},

=3:

=3,𝑛 𝑛+1 𝑛+1

𝑛+1

n+1,n+1.

{a}}n+1=a{c}=b.{a}{c};

b=am,

m

.

n+1

=2

=b

=2

=2

=b

=2

b

=2

b

,

m

.

{a}=★*. {a

},

=

=a

q

=𝑛(𝑛-11)+

.

b

=b=b{c},{c}

q=𝑐𝑐

=cq=2×2=2.

=b=2

b=2

b=2

b=am,

{a};

b=a}

n

,

n

.{a}

=aq=2

b=a+n-6=n-6+2,

+2++2𝑛

n

n

,𝑛(𝑛-11)

,

n=4

=

n=3

=

n=2

=

n=1

=

n

{a

}

1

2

=𝑎1(1-𝑞

=1-3

= {a

}

1

2

=𝑎1(1-𝑞

=1-3

=1

=-4

=-4q,

q=1

q=-1,qq=-1,=𝑎+a{a};

n

.

+a𝑎

𝑎1𝑞

𝑎1𝑞

3q+3q

q

q=3

=a

{a}

=aq=3★*.{a},𝑛1-𝑞𝑛 2

12

n★*,

n

{a}

,

,

=a{a}

n

.

q

{a};

n

.

,+a=2a,22 𝑞

n

=32(-

1

𝑛-1

,

n

,

m}

m

Tm=-

m+

{a

}

{

=

=5★*.

m}

m

Tm=-

m+

{a

}

{

=

=5★*.

=

𝑎𝑛

[

(

)

]

=

[1-(

)

],𝑚

+

++

=𝑎 𝑎 𝑎𝑚 (

)

[1-(

)

]<

={(-