2021版數(shù)學攻略大一輪復習 6.3 等比數(shù)列(試題部分)

年考情考點 內(nèi)容解讀

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數(shù)列的

考題示例

考向

關(guān)聯(lián)考點

有關(guān)概念及運

n

n

★★★

性質(zhì)及

★★★

.,,.

n

,

,,.,.

考點一 等比數(shù)列的有關(guān)概念及運算

{a},

=

q= +a++a=

{a},

=

q= +a++a= .

{a}

=

n+1 n+2 A

{a},

= . 考點二 等比數(shù)列的性質(zhì)及應用

,

,

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,?? .??

,,,,,,.

,, .

=p-2,

=a

=a

+a

=a

+a

+a

{a}

n

=p-2,

n★*.

p

{a};{????}},.

{a},

q=??=,????

??????+1=

=,??2??????+1=

=,??2??{????

}

=a

+a

++a

,

,{a}

=aq=2★*

:{????},}:????=4, 2-??3-??

=n×2,}

,}

=,

,

=,

,

=

????{a}

,

??

,

{a}

n

=1+,

{a},; 1-??

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

n+1=n+1,

n+1.

????+1=

??

.??-11-?? ??-1

=

(

??

)

??-1

=1-(

??

)

.

=

(

??

)

=,(

??

)

=

,n+1

n+1

,,??-15 5 ??-1 ??-1

n+1

n+1

,

A

考點一 等比數(shù)列的有關(guān)概念及運算

{a}}

=b=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.??

,,.,.考點二 等比數(shù)列的性質(zhì)及應用 ,

.

,,,. A.

B.

5 7 B

考點一 等比數(shù)列的有關(guān)概念及運算

:,,,:,

,

B

5

{a}

n

.

=,??=a,

=

.

{a}

{a}

n+1.

b=

??.??=.n+1 ??+1 =?? 2????,

bn+1=2b,

??=2,

=n.??

,

=

.

{a}

+a

= . ??

b;},;{a}.

??

n=1

=4a,

n=2

=3a,

b}

.??+1 ??

b}

.??

{a}=4a.{a};

{a}

n

.

m

.{a}

=q.

q=4q,

q=-2

=2.??

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+q??

??

??

),??

}

b=2.

b=21

q

q=-5

q=-5,

q=4

,

考點二 等比數(shù)列的性質(zhì)及應用

{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}.

=??(1-??

=-

n+2n+1=-

1-??

??+3??+2

??

??+1

.=2[-

=2[-

??

??+1

],.

=a

n

:S.

=a

n

:S

=(??+????=na

+??(??-1)

=a

q.

n

:S

=??

(1-???? ::n+1 ::????+1=q(q.???? ????

1-??

,:??+??=b

c=b.

,

bd

,2??+?? 2??+?? B.

B

{a}

d

,

.

,

,

,

{a}<a<a A. B.

{a}

,

n

.

{a}

,

n

.

=

,

??

??

??+1

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

=.

,n+1=3n+1=,+3=??+1

,

{a}{a}

n

= . = = . ;

{a}

+a+a

.

{a},

n+1=2.

q

;{a}

n

,n+1.??

-??

??-??

{a},??

-??

=aq-a

=3.,

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

=3:

=3,?? ??+1 ??+1

??+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

=??(??-11)+

.

b

=b=b{c},{c}

q=????

=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++2??

n

n

,??(??-11)

,

n=4

=

n=3

=

n=2

=

n=1

=

n

{a

}

1

2

=??1(1-??

=1-3

= {a

}

1

2

=??1(1-??

=1-3

=1

=-4

=-4q,

q=1

q=-1,qq=-1,=??+a{a};

n

.

+a??

??1??

??1??

3q+3q

q

q=3

=a

{a}

=aq=3★*.{a},??1-???? 2

12

n★*,

n

{a}

,

,

=a{a}

n

.

q

{a};

n

.

,+a=2a,22 ??

n

=32(-

1

??-1

,

n

,

m}

m

Tm=-

m+

{a

}

{

=

=5★*.

m}

m

Tm=-

m+

{a

}

{

=

=5★*.

=

????

[

(

)

]

=

[1-(

)

],??

+

++

=?? ?? ???? (

)

[1-(

)

]<

={(-