Find the first four terms and the 100th term of the sequence whose nth term is given.
an = (−1)n + 1
n
n + 1
a1 =
a2 =
a3 =
a4 =
a100 =
To find the first four terms of the sequence whose nth term is given by an = (-1)n + 1 / (n + 1), we can substitute the values of n from 1 to 4 into the equation.
a1 = (-1)^1 + 1 / (1 + 1) = -1 + 1 / 2 = -1 + 1/2 = -1/2
a2 = (-1)^2 + 1 / (2 + 1) = 1 + 1 / 3 = 1 + 1/3 = 4/3
a3 = (-1)^3 + 1 / (3 + 1) = -1 + 1 / 4 = -1 + 1/4 = -3/4
a4 = (-1)^4 + 1 / (4 + 1) = 1 + 1 / 5 = 1 + 1/5 = 6/5
So, the first four terms of the sequence are:
a1 = -1/2
a2 = 4/3
a3 = -3/4
a4 = 6/5
To find the 100th term of the sequence, we substitute n = 100 into the equation.
a100 = (-1)^100 + 1 / (100 + 1) = 1 + 1 / 101 = 1 + 1/101 = 102/101
Therefore, the 100th term of the sequence is 102/101.
To find the first four terms and the 100th term of the sequence whose nth term is given by an = (-1)^(n + 1) / (n + 1), we substitute the values of n and calculate the corresponding terms:
a1 = (-1)^(1 + 1) / (1 + 1) = 1/2
a2 = (-1)^(2 + 1) / (2 + 1) = -1/3
a3 = (-1)^(3 + 1) / (3 + 1) = 1/4
a4 = (-1)^(4 + 1) / (4 + 1) = -1/5
a100 = (-1)^(100 + 1) / (100 + 1) = 1/101
Therefore, the first four terms of the sequence are: a1 = 1/2, a2 = -1/3, a3 = 1/4, a4 = -1/5.
And the 100th term of the sequence is a100 = 1/101.