Find the first five terms of the sequence whose nth term is given.
a: (-2)n + 2n
b: n squared(-1)n
c: |10-n squared|
what, you have a problem evaluating expressions?
(-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 the given sequences, we substitute the values of n from 1 to 5.
a) For the sequence a: (-2)^n + 2n:
Substituting n = 1, 2, 3, 4, 5:
a_1 = (-2)^1 + 2(1) = -2 + 2 = 0
a_2 = (-2)^2 + 2(2) = 4 + 4 = 8
a_3 = (-2)^3 + 2(3) = -8 + 6 = -2
a_4 = (-2)^4 + 2(4) = 16 + 8 = 24
a_5 = (-2)^5 + 2(5) = -32 + 10 = -22
Therefore, the first five terms of sequence a are 0, 8, -2, 24, -22.
b) For the sequence b: n^2(-1)^n:
Substituting n = 1, 2, 3, 4, 5:
b_1 = 1^2(-1)^1 = 1(-1) = -1
b_2 = 2^2(-1)^2 = 4(1) = 4
b_3 = 3^2(-1)^3 = 9(-1) = -9
b_4 = 4^2(-1)^4 = 16(1) = 16
b_5 = 5^2(-1)^5 = 25(-1) = -25
Therefore, the first five terms of sequence b are -1, 4, -9, 16, -25.
c) For the sequence c: |10 - n^2|:
Substituting n = 1, 2, 3, 4, 5:
c_1 = |10 - 1^2| = |10 - 1| = |9| = 9
c_2 = |10 - 2^2| = |10 - 4| = |6| = 6
c_3 = |10 - 3^2| = |10 - 9| = |1| = 1
c_4 = |10 - 4^2| = |10 - 16| = | -6| = 6
c_5 = |10 - 5^2| = |10 - 25| = | -15| = 15
Therefore, the first five terms of sequence c are 9, 6, 1, 6, 15.
To find the first five terms of a given sequence, we substitute values of n starting from 1 and calculate the corresponding nth term. Let's solve each sequence step by step:
a: (-2)^n + 2n
For n = 1: (-2)^1 + 2(1) = -2 + 2 = 0
For n = 2: (-2)^2 + 2(2) = 4 + 4 = 8
For n = 3: (-2)^3 + 2(3) = -8 + 6 = -2
For n = 4: (-2)^4 + 2(4) = 16 + 8 = 24
For n = 5: (-2)^5 + 2(5) = -32 + 10 = -22
The first five terms of sequence a are 0, 8, -2, 24, -22.
b: n^2(-1)^n
For n = 1: 1(-1)^1 = 1(-1) = -1
For n = 2: 2^2(-1)^2 = 4(1) = 4
For n = 3: 3^2(-1)^3 = 9(-1) = -9
For n = 4: 4^2(-1)^4 = 16(1) = 16
For n = 5: 5^2(-1)^5 = 25(-1) = -25
The first five terms of sequence b are -1, 4, -9, 16, -25.
c: |10 - n^2|
For n = 1: |10 - 1^2| = |10 - 1| = 9
For n = 2: |10 - 2^2| = |10 - 4| = 6
For n = 3: |10 - 3^2| = |10 - 9| = 1
For n = 4: |10 - 4^2| = |10 - 16| = 6
For n = 5: |10 - 5^2| = |10 - 25| = 15
The first five terms of sequence c are 9, 6, 1, 6, 15.