在等比数列{an}中，已知a1=3，a4=24. （1）求公比q的值； （2）求S4 在等比数列{an}中，已知a1＝3，a9＝8a6，求s4.
\u5df2\u77e5\u7b49\u6bd4\u6570\u5217{an}\u4e2d\uff0ca2=3\uff0ca6=243\uff0c\uff081\uff09\u6c42a4\u7684\u503c\uff0c\uff082\uff09\u6c42\u6570\u5217{an}\u7684\u901a\u9879\u516c\u5f0f\uff081\uff09\u2235a4\u4e3aa2\u548ca6\u7684\u7b49\u6bd4\u4e2d\u9879\uff0c\u53c8a4\uff1da2q2\uff1e0\uff0c\u2234a4\uff1da2a6\uff1d27\uff0e\uff082\uff09\u2235a6a2\uff1dq4\uff0c\u2234q4\uff1d2433\uff1d81\uff0cq=\u00b13\uff1b\u5f53q=3\u65f6\uff0ca1\uff1da2q\uff1d1\uff0c\u2234an\uff1d3n?1\uff0e\u5f53q=-3\u65f6\uff0ca1\uff1da2q\uff1d?1\uff0c\u2234an\uff1d?(?3)n?1\uff0e
\u89e3\uff1a\u8bbe\u7b49\u6bd4\u6570\u5217{a
n
}\u7684\u516c\u6bd4\u4e3aq\uff08q
\u2260
0\uff09\uff0c\u56e0\u6b64a
n
=
a
1
q
n-1
=
3q
n-1
\uff0cn\u2208N
*
\uff0c\u6240\u4ee5\u6709a
9
=
3q
8
\uff0c\u800c\u4e14a
6
=
3q
5
\uff0c\u7531\u5df2\u77e5a
9
=
8a
6
\uff0c\u6240\u4ee53q
8
=
8*3q
5
=
24q
5
\uff0c\u6240\u4ee5q
3
=
8\uff0c\u6545q
=
3
\u221a8
=
2\uff0c\u6240\u4ee5a
n
=
3*2
n-1
\uff0c\u8ba1\u7b97\u5f97a
2
=
3*2
=
6\uff0ca
3
=
3*2
2
=
12\uff0ca
4
=
3*2
3
=
24\uff0c\u7528S
n
\u8868\u793a\u6570\u5217{a
n
}\u524dn\u9879\u7684\u548c\uff0c\u6240\u4ee5S
4
=
a
1
+
a
2
+
a
3
+
a
4
=
3
+
6
+
12
+
24
=
45\uff0c\u5373
S
4
=
45
\u3002
∵a4=a1q³
∴q³=a4/a1=24/3=8
即q=2
（2）
a2=a1q=3x2=6
a3=a2q=6x2=12
S4=a1+a2+a3+a4
=3+6+12+24
=45
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a4=a1*（q的三次方）
即24=3*（q的三次方）
q=2
a1=3,a2=6,a3=12,a4=24
所以S4=45
。
q=2
a1=3 a2=6 a3==12 a4=24
S4=3+6+12+24=45
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