已知数列{an}是公差不为零的等差数列,数列{abn}是公比为q的等比数列,且b1=1b2=10b3=46,求公比q及bn

Question

已知数列{an}是公差不为零的等差数列,数列{abn}是公比为q的等比数列,且b1=1 b2=10
b3=46,求公比q及bn

Answer 1

a1,a10,a46为等比数列,∴(a1+9d)^2=a1(a1+45d).
∴a1=3d.所以an=(n+2)d.
a1=3d,a10=12d,∴q=4.
abn=(bn+2)d=3dq^(n-1)
∴bn=3×4^(n-1)-2.
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