等差数列{an}的前n项和记为Sn.以已知a10=30,a20=50.令bn=2^(an-10),求数列{bn}的前n项和Tn

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等差数列{an}的前n项和记为Sn.以已知a10=30,a20=50.令bn=2^(an-10),求数列{bn}的前n项和Tn
等差数列{an}的前n项和记为Sn.以已知a10=30,a20=50.令bn=2^(an-10),求数列{bn}的前n项和Tn

等差数列{an}的前n项和记为Sn.以已知a10=30,a20=50.令bn=2^(an-10),求数列{bn}的前n项和Tn
A20-A10=50-30=20=10d
d=2
A1=A10-9d=30-18=12
An=A1+(n-1)d=12+2(n-1)=2n+10
(An)-10=2n
Bn=2^(An-10)
=2^(2n)
=4^n
{Bn}是等比数列
Tn=B1×(1-q^n)/(1-q)
=4×(1-4^n)/(1-4)
=(4/3)×(4^n-1)

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