Find the first five terms of the sequence whose nth term is given.
a: (-2)^n + 2^n
b: n^2(-1)^n
c: |10 - n^2|
(-2)^n+2n: -2+2, 4+4, -8+6, 16+8, ...
n^2(-1)^n: -1, +4, -9, ...
|10-n^2|: |10-1|, |10-4|, |10-9|, ...
To find the first five terms of each sequence, we can substitute the values of n from 1 to 5 into the formulas given for each sequence.
a: (-2)^n + 2^n
For the first five terms, when n = 1, 2, 3, 4, and 5:
a1 = (-2)^1 + 2^1 = -2 + 2 = 0
a2 = (-2)^2 + 2^2 = 4 + 4 = 8
a3 = (-2)^3 + 2^3 = -8 + 8 = 0
a4 = (-2)^4 + 2^4 = 16 + 16 = 32
a5 = (-2)^5 + 2^5 = -32 + 32 = 0
The first five terms of the sequence a are: 0, 8, 0, 32, 0.
b: n^2(-1)^n
For the first five terms, when n = 1, 2, 3, 4, and 5:
b1 = 1^2(-1)^1 = 1 * -1 = -1
b2 = 2^2(-1)^2 = 4 * 1 = 4
b3 = 3^2(-1)^3 = 9 * -1 = -9
b4 = 4^2(-1)^4 = 16 * 1 = 16
b5 = 5^2(-1)^5 = 25 * -1 = -25
The first five terms of the sequence b are: -1, 4, -9, 16, -25.
c: |10 - n^2|
For the first five terms, when n = 1, 2, 3, 4, and 5:
c1 = |10 - 1^2| = |10 - 1| = |9| = 9
c2 = |10 - 2^2| = |10 - 4| = |6| = 6
c3 = |10 - 3^2| = |10 - 9| = |1| = 1
c4 = |10 - 4^2| = |10 - 16| = |-6| = 6
c5 = |10 - 5^2| = |10 - 25| = |-15| = 15
The first five terms of the sequence c are: 9, 6, 1, 6, 15.