Answer 1

a_n = (−1)ⁿ 2ⁿ

Here, the n^th term is given by the above expression. So, to find the first term we use n = 1 we get

`a_1 = (-1)^1.2^(1)`

= (-1).2

= -2

Similarly, we find the other four terms,

Second term (n = 2)

`a_2 = (-1)^2.2^2`

= 1.4

= 4

Third term (n = 3)

`a_3 = (-1)^3 . 2^3`

= (-1).8

= -8

Fourth term (n = 4)

`a_4 = (-1)^4 . 2^4`

= 1.16

= 16

Fifith term (n = 5)

`a_3 = (-1)^5 . (2)^5`

= (-1). 32

= -32

Therefore, the first five terms of the given A.P are `a_1 = -2, a_2 = 4, a_3 = -8, a_4 = 16, a_5 = -32`