已知等比数列{an}中,a2=2,a5=128. (1)求通项an; (2)若bn=log2an,数列{bn}的前n项和为Sn,且Sn=360,求n的值.
问题描述:
已知等比数列{an}中,a2=2,a5=128.
(1)求通项an;
(2)若bn=log2an,数列{bn}的前n项和为Sn,且Sn=360,求n的值.
答
(1)设公比为q,由a2=2,a5=128及a5=a2q3得 128=2q3,∴q=4∴an=a2qn-2=2•4n-2=22n-3(6分)(2)∵bn=log222n-3=2n-3,∴数列{bn}是以-1为首项,2为公差的等差数列∴Sn=n(-1)+n(n−1)2•2=n2-2n令n2-2n=36...