Hi! I need help with these two questions. Thanks!
1.) Look for the first four terms for the following sequence below.
an=n(n^2-6)
2.) For this question, remember that your answer has to begin with the second term of the following sequence. Look for the next four terms of the following sequence defined recursively.
a1=14
an+1=(-2)an
what, you can't plug in values for n?
a1 = 1(1^2-6) = 1(-5) = -5
a2 = 2(2^2-6) ...
a1=14
a2 = (-2)(14) = -28
a3 = (-2)(-28) ...
Sure! I can help you with both of these questions. Let's start with the first one.
1.) To find the first four terms of the sequence described by the formula an = n(n^2-6), we need to substitute values of n into the formula.
First term: n = 1
a1 = 1(1^2-6) = 1(1-6) = 1(-5) = -5
Second term: n = 2
a2 = 2(2^2-6) = 2(4-6) = 2(-2) = -4
Third term: n = 3
a3 = 3(3^2-6) = 3(9-6) = 3(3) = 9
Fourth term: n = 4
a4 = 4(4^2-6) = 4(16-6) = 4(10) = 40
So, the first four terms of the sequence are -5, -4, 9, and 40.
Now let's move on to the second question.
2.) The sequence defined recursively with a1 = 14 and an+1 = (-2)an means that each term is obtained by multiplying the previous term by -2.
To find the next four terms, we can start with the given first term and use the recursive formula to calculate the following terms.
Second term: a1 = 14
a2 = (-2)a1 = (-2)(14) = -28
Third term: a2 = -28
a3 = (-2)a2 = (-2)(-28) = 56
Fourth term: a3 = 56
a4 = (-2)a3 = (-2)(56) = -112
Fifth term: a4 = -112
a5 = (-2)a4 = (-2)(-112) = 224
So, the next four terms of the sequence are -28, 56, -112, and 224.
I hope this helps! Let me know if you have any further questions.