I need some help I posted the first question to this a bit ago but didn't enter it correctly so sorry to those who helped! I also have a 2nd half which I understood till they added the dividing part.
I need to find the first five terms of each recursive sequence.
1.C1=64, C2=32
Cn= Cn-2 - Cn-1/2
Next!! Find the indicated partial sum for each sequence.
2. An=1/n; S5
3. An= n/n+1;S4
No problem! I'm here to help you. Let's go through the questions step by step.
1. To find the first five terms of the recursive sequence, you can use the given formula: Cn = Cn-2 - Cn-1/2.
Start with the given initial values C1 = 64 and C2 = 32.
- For n = 3:
C3 = C1 - C2/2
= 64 - 32/2
= 64 - 16
= 48
- For n = 4:
C4 = C2 - C3/2
= 32 - 48/2
= 32 - 24
= 8
- For n = 5:
C5 = C3 - C4/2
= 48 - 8/2
= 48 - 4
= 44
So, the first five terms of the sequence are 64, 32, 48, 8, 44.
2. Now, let's move on to the second question: Find the indicated partial sum for each sequence.
For the sequence An = 1/n, and S5 means the sum of the first 5 terms of the sequence.
To find the partial sum, you'll need to add the terms of the sequence up to the given number. In this case, you need to find the sum of the first 5 terms (S5).
- For n = 1:
A1 = 1/1 = 1
- For n = 2:
A2 = 1/2 = 0.5
- For n = 3:
A3 = 1/3 = 0.33
- For n = 4:
A4 = 1/4 = 0.25
- For n = 5:
A5 = 1/5 = 0.2
To find the partial sum S5, you'll add all these terms together:
S5 = A1 + A2 + A3 + A4 + A5
= 1 + 0.5 + 0.33 + 0.25 + 0.2
= 2.28
So, the indicated partial sum for the sequence An = 1/n with S5 is 2.28.
3. Moving on to the last question: Find the indicated partial sum for the sequence An = n/(n+1), and S4 means the sum of the first 4 terms of the sequence.
- For n = 1:
A1 = 1/(1+1) = 1/2 = 0.5
- For n = 2:
A2 = 2/(2+1) = 2/3 = 0.67
- For n = 3:
A3 = 3/(3+1) = 3/4 = 0.75
- For n = 4:
A4 = 4/(4+1) = 4/5 = 0.8
To find the partial sum S4, you'll add all these terms together:
S4 = A1 + A2 + A3 + A4
= 0.5 + 0.67 + 0.75 + 0.8
= 2.72
So, the indicated partial sum for the sequence An = n/(n+1) with S4 is 2.72.