Reiny can you please help with these 3 problem. 1. a1=-4;an-1-3 this is find the first five terms of the recursively defined sequence. Problem 2 and 3 is write the first terms of the explicitly defined sequence an=4n+2. problem 3 an=2(-3)n-1
You seem to be persistent in writing your problem in a way that makes no sense.
Again, I will assume you mean:
a(1) = -4
a(n) = a(n-1) - 3
often this is written with subscripts
a1 = -4
an = an-1 - 3
so
a1 = -4
a2 = a1 - 3 = -4-3 = -7
a3 = a2 - 3 = -7-3 = =10
continue this pattern for 2 more terms
problems 2 and 3 make no sense to me
I thought these were recursively defined sequences. In that case the initial term must be defined, since each new term is found from its previous term.
With no brackets, who can tell what they mean.
problem 2 and problem 3 is to write the first terms of the explicitly defined sequences. problem 2: a(n)=4n+2. and problem 3: a(n)=2(-3)n-1.
i need to write the first five
Sure! I can help you with these problems.
Problem 1: Finding the first five terms of the recursively defined sequence with a1 = -4 and an-1 = -3.
To find the first five terms of this sequence, we can use the recursive formula. Here's how to do it:
Step 1: Start with the given value of a1, which is -4. This will be our first term.
Step 2: Use the recursive formula an-1 = -3 to find the next term. Substitute the value of n-1 with 1 (as we have already found the first term).
an = an-1 - 3
a2 = a1 - 3
a2 = -4 - 3
a2 = -7
So, the second term of the sequence is -7.
Step 3: Repeat the process to find the next terms. Use the formula an = an-1 - 3 and substitute n-1 with the appropriate value.
a3 = a2 - 3
a3 = -7 - 3
a3 = -10
The third term is -10.
a4 = a3 - 3
a4 = -10 - 3
a4 = -13
The fourth term is -13.
a5 = a4 - 3
a5 = -13 - 3
a5 = -16
The fifth term is -16.
Therefore, the first five terms of the sequence are: -4, -7, -10, -13, -16.
Now, let's move on to problems 2 and 3.
Problem 2: Writing the first terms of the explicitly defined sequence an = 4n + 2.
To find the first terms of this sequence, we can substitute different values of n into the equation to calculate the corresponding terms. Here's how to do it:
When n = 1:
a1 = 4(1) + 2
a1 = 4 + 2
a1 = 6
So, the first term is 6.
When n = 2:
a2 = 4(2) + 2
a2 = 8 + 2
a2 = 10
The second term is 10.
When n = 3:
a3 = 4(3) + 2
a3 = 12 + 2
a3 = 14
The third term is 14.
Therefore, the first three terms of the sequence are: 6, 10, 14.
Moving on to problem 3.
Problem 3: Writing the first terms of the explicitly defined sequence an = 2(-3)^(n-1).
Similar to problem 2, we can find the first terms of this sequence by substituting different values of n into the equation. Here's how you can do it:
When n = 1:
a1 = 2(-3)^(1-1)
a1 = 2(-3)^0
a1 = 2(1)
a1 = 2
So, the first term is 2.
When n = 2:
a2 = 2(-3)^(2-1)
a2 = 2(-3)^1
a2 = 2(-3)
a2 = -6
The second term is -6.
When n = 3:
a3 = 2(-3)^(3-1)
a3 = 2(-3)^2
a3 = 2(9)
a3 = 18
The third term is 18.
Therefore, the first three terms of the sequence are: 2, -6, 18.
I hope this helps! Let me know if you have any further questions.