a_n=-2n(n+3)

Question

Find the first five terms of the sequence defined by the explicit form

Answer 1

To find the first five terms of the sequence defined by the explicit form a_n = -2n(n+3), we substitute the values 1, 2, 3, 4, and 5 into the equation.

For n = 1:
a_1 = -2(1)(1+3) = -2(1)(4) = -8

For n = 2:
a_2 = -2(2)(2+3) = -2(2)(5) = -20

For n = 3:
a_3 = -2(3)(3+3) = -2(3)(6) = -36

For n = 4:
a_4 = -2(4)(4+3) = -2(4)(7) = -56

For n = 5:
a_5 = -2(5)(5+3) = -2(5)(8) = -80

Therefore, the first five terms of the sequence defined by the explicit form are:

-8, -20, -36, -56, -80