Question

Write out the first five terms of the sequence with, [ n+3n ] n=1/[infinity] , determine whether the sequence corverges, and if so find its limit.

Enter the following information for a n = n+3n
a 1 =
a 2 =
a 3 =
a 4 =
a5=
​Does the sequence converge = _______ ( yes/no)

Answer 1

The first five terms of the sequence are 1, 4, 9, 16, and 25 respectively. The sequence, defined by the nth term formula an = n2, does not converge as it diverges to infinity.

Step-by-step explanation:

The question involves a sequence where the nth term (an) is given by an expression that simplifies to n2. To find the first five terms of this sequence, we substitute the values of n starting with 1 and continue until we reach 5.

1. For n=1: a1 = 12 = 1
2. For n=2: a2 = 22 = 4
3. For n=3: a3 = 32 = 9
4. For n=4: a4 = 42 = 16
5. For n=5: a5 = 52 = 25

To determine if the sequence converges, we look at the behavior of the terms as n approaches infinity. Since the terms n2 grow without bound, the sequence does not converge; instead, it diverges to infinity.