Question

已知公差不為零的等差數(shù)列的第k、n、p項(xiàng)構(gòu)成等比數(shù)列的連續(xù)三項(xiàng)，則等比數(shù)列的公比為（　�。�

• A．

  n-p

  k-n

• B．

  p-n

  p-k

• C．

  n-k

  n-p

• D．

  k-p

  n-p

Answer 1

分析：設(shè)首項(xiàng)和公差，由等比數(shù)列的性質(zhì)可知q=

an

ak

=

ap

an

=

ap-an

an-ak

，然后利用等差數(shù)列的通項(xiàng)公式化簡(jiǎn)即可．

解答：解：設(shè)等差數(shù)列首項(xiàng)為a₁，公差為d，則
q=

an

ak

=

ap

an

=

ap-an

an-ak

=

[a1+(p-1)d]-[a1+(n-1)d]

[a1+(n-1)d]-[a1+(k-1)d]

=

p-n

n-k

=

n-p

k-n

．
故選A．

點(diǎn)評(píng)：此題考查了等比數(shù)列和等差數(shù)列的性質(zhì)，屬于基礎(chǔ)題．