Question

數(shù)列-

1

3×5

，

2

5×7

，-

3

7×9

，

4

9×11

，…的通項(xiàng)為（　�。�

• A．(-1)n+1

  1

  (2n+1)(2n+3)

• B．(-1)n+1

  n

  (2n+1)(2n+3)

• C．(-1)n

  1

  (2n+1)(2n+3)

• D．(-1)n

  n

  (2n+1)(2n+3)

Answer 1

分析：先寫出數(shù)列前幾項(xiàng)的值與項(xiàng)的關(guān)系即可總結(jié)通項(xiàng)公式

解答：解：由題意可知，a₁=-

1

3×5

=(-1)1

1

(2×1+1)(2×2+1)

，a2=

2

5×7

=（-1）²

2

(2×2+1)(2×3+1)

a₃=

3

7×9

=(-1)3

3

(2×3+1)(2×4+1)

…
an=(-1)n

n

(2n+1)(2n+3)

故選D

點(diǎn)評(píng)：本題主要考查了數(shù)列的通項(xiàng)公式的求解，解題的關(guān)鍵是發(fā)現(xiàn)數(shù)列項(xiàng)的規(guī)律