Find the first four terms and the 100th term of the sequence whose nth term is given.
an = n2 − 6
a1 =
a2 =
a3 =
a4 =
a100 =
a1 = 1^2 - 6 = -5
a2 = 2^2 - 6 = -2
a3 = 3^2 - 6 = 3
a4 = 4^2 - 6 = 10
To find the 100th term, substitute n = 100 into the formula:
a100 = 100^2 - 6 = 10,000 - 6 = 9,994
To find the first four terms of the sequence, we substitute in different values of n into the given formula.
a1 = 1^2 - 6 = 1 - 6 = -5
a2 = 2^2 - 6 = 4 - 6 = -2
a3 = 3^2 - 6 = 9 - 6 = 3
a4 = 4^2 - 6 = 16 - 6 = 10
Therefore, the first four terms of the sequence are:
a1 = -5
a2 = -2
a3 = 3
a4 = 10
To find the 100th term, we substitute n = 100 into the given formula:
a100 = 100^2 - 6 = 10000 - 6 = 9994
Therefore, the 100th term of the sequence is a100 = 9994.