Question

Find the indicated terms in the following sequences whose nth terms are:

a_n = (n − 1) (2 − n) (3 + n); a₁, a₂, a₃

Answer 1

a_n = (n − 1) (2 − n) (3 + n)

We need to find `a_1, a_2, and a_3`

Now, to find  `a_1` term we use n = 1 we get

`a_1 = (1 - 1)(2- 1)(3 + 1)`

= (0)(1)(4)

= 0

Also to find `a_2` term we use n = 2 we get

`a_2 = (2 - 1)(2 - 2)(3 + 2)`

= (1)(0)(5)

= 0

Similarly, to find `a_3` term we use n = 3 we get

`a_3 = (3 -1)(2 - 3)(3 + 3)`

= (2)(-1)(6)

= -12

Thus `a_1 = 0, a_2 = 0` and `a_3 = -12`