Question

Write the first five terms of the sequence defined by the explicit formula an=-4n(n-1)

Answer 1

The explicit formula of the sequence is given by a_n = -4n(n-1).

We have to find the first five terms of the sequence.

The first term:

$\begin{gathered} a_1=-4\times(1)(1-1) \\ =-4(0) \\ =0 \end{gathered}$

The second term:

$\begin{gathered} a_2=-4(2)(2-1) \\ =-8(1) \\ =-8 \end{gathered}$

The third sum:

$\begin{gathered} a_3=-4(3)(3-1) \\ =-12(2) \\ =-24 \end{gathered}$

The fourth term:

$\begin{gathered} a_4=-4(4)(4-1) \\ =-16(3) \\ =-48 \end{gathered}$

The fifth term:

$\begin{gathered} a_5=-4(5)(5-1) \\ =-20(4) \\ =-80 \end{gathered}$

Thus, option D is correct.