Write the first five terms of the sequence defined by the recursive formula a(n) = 2*(a(n - 1)) + 5 with a(1) = -3
-3, -10, -24, -43, -81
-3, -1, 3, 11, 27
-3, 2, 7, 12, 17
-3, 4, 18, 46, 102
I'm trying to do this the way I've always done them (and gotten them right in the past) but I keep getting it wrong:(
a(n) = 2*(a(n-1)) + 5
a(1) = -3
a(2) = 2*(a(2-1)) + 5
= 2*(a(1)) + 5
= 2*(-3) + 5
= -1
Basically, you take the previous value and plug it in the given formula to obtain the next value.
B is -3,-1,3.. is correct 100%
Well, I must say your sequence is certainly... unique. It seems like you might've tripped over a clown shoe there. But fear not, I'll help you out.
Let's break it down step by step. The recursive formula a(n) = 2*(a(n - 1)) + 5 tells us that each term in the sequence is obtained by multiplying the previous term by 2, and then adding 5 to it.
Starting with a(1) = -3, we can apply the formula to find the next term:
a(2) = 2*(a(1)) + 5 = 2*(-3) + 5 = -1
Continuing on to find a(3) using a(2):
a(3) = 2*(a(2)) + 5 = 2*(-1) + 5 = 3
Let's keep the clown party going and find a(4):
a(4) = 2*(a(3)) + 5 = 2*(3) + 5 = 11
One last step to complete our circus act and find a(5):
a(5) = 2*(a(4)) + 5 = 2*(11) + 5 = 27
So, the first five terms of the sequence are: -3, -1, 3, 11, 27. Now you can dazzle the audience with your newfound sequence knowledge!
To find the first five terms of a sequence defined by a recursive formula, you can use the given recursive formula and initial value.
In this case, the recursive formula is a(n) = 2*(a(n - 1)) + 5 and a(1) = -3.
To find the first term, substitute n = 1 into the formula:
a(1) = 2*(a(1 - 1)) + 5
a(1) = 2*(a(0)) + 5
Since the formula depends on a(0), we need to find the value of a(0) to proceed.
Given that a(1) = -3, we can substitute n = 1 into the recursive formula:
-3 = 2*(a(1 - 1)) + 5
-3 = 2*(a(0)) + 5
Solving this equation for a(0), we have:
-3 = 2a(0) + 5
2a(0) = -8
a(0) = -4
Now, with the initial value a(0) = -4, we can find the remaining terms in the sequence using the recursive formula.
a(2) = 2*(a(2 - 1)) + 5
a(2) = 2*(a(1)) + 5
Substituting a(1) = -3, we have:
a(2) = 2*(-3) + 5
a(2) = -6 + 5
a(2) = -1
a(3) = 2*(a(3 - 1)) + 5
a(3) = 2*(a(2)) + 5
Substituting a(2) = -1, we have:
a(3) = 2*(-1) + 5
a(3) = -2 + 5
a(3) = 3
a(4) = 2*(a(4 - 1)) + 5
a(4) = 2*(a(3)) + 5
Substituting a(3) = 3, we have:
a(4) = 2*(3) + 5
a(4) = 6 + 5
a(4) = 11
a(5) = 2*(a(5 - 1)) + 5
a(5) = 2*(a(4)) + 5
Substituting a(4) = 11, we have:
a(5) = 2*(11) + 5
a(5) = 22 + 5
a(5) = 27
Therefore, the first five terms of the sequence, using the recursive formula a(n) = 2*(a(n - 1)) + 5 with a(1) = -3, are: -3, -1, 3, 11, 27.