# Thread: Find the first 5 terms

1. ## Find the first 5 terms

Find the first five terms of the recursively defined sequences bellow,

a. a1 = 1, an+1=1 + 1/n

b. a1=2, a2=3,a3= 4, an-1 + an-3

c. a1=2, an+1=an!

2. What have you done?
Where do you have a problem?
There are very straight forward!

3. uhm.. for a. what does it mean by 'first 5 terms?' is that n+1, n+2.. n+5?
for b. what are the first 5 terms...? anf for c. also i dont know what the first 5 terms are

4. Originally Posted by arturju
Find the first five terms of the recursively defined sequences bellow,

a. a1 = 1, an+1=1 + 1/n
Originally Posted by arturju
uhm.. for a. what does it mean by 'first 5 terms?' is that n+1, n+2.. n+5?
for b. what are the first 5 terms...? anf for c. also i dont know what the first 5 terms are
I'll do the first one as an example and I would recommend you do the other two and post them. That way we can check your work and correct any mistakes you may have made.

a) a_1 = 1, a_{n+1} = 1 + 1/n

In general this series is defined as the set of numbers:
a_1, a_2, a_3, ...

The first 5 terms of the series would then be:
a_1, a_2, a_3, a_4, and a_5.

By the definition above, the first term, a_1, is given by
a_1 = 1.

Again, by the definition above, a_2 is given by the n = 2 term a_n = 1 + 1/n for n = 2. So:
a_2 = 1 + 1/2 = 3/2

Similarly
a_3 = 1 + 1/3 = 4/3

a_4 = 1 + 1/4 = 5/4

a_5 = 1+ 1/5 = 6/5

So the first five terms of the series are:
1, 3/2, 4/3, 5/4, and 6/5.

You should consult your textbook to make sure you understand what the different words mean (such as what a "term" of a series is) to help you out.

-Dan

5. if the first five terms for the 1st one are as you said, then for the 2nd one wouldnt i have tu find just the next one?
Nevertheless, i worked on the problem and i got this:

b. a1=2, a2=3,a3= 4, an-1 + an-3

~~~~~~~~~~~~~~~~~~~~~
a4=a4-1+a4-3=4+2=6
a5=a5-1+a5-3=6+3=9
a6=a6-1+a6-3=9+4=13
a7=a7-1+a7-3=13+6=19
...and so on..
I think i did problem c. wrong but i'll post it here anyways:
c. a1=2, an+1=an!
~~~~~~~~~~~~~~~~~~~~~
a2=a1+1=a1!=2
a3=a2+1=a2!=2
... and so i got 2 for all of them..
I have another problem like this i'm having trouble with but i'd rather post it after i get this one over with. Thx in advance

6. Originally Posted by arturju
if the first five terms for the 1st one are as you said, then for the 2nd one wouldnt i have tu find just the next one?
Nevertheless, i worked on the problem and i got this:

b. a1=2, a2=3,a3= 4, an-1 + an-3

~~~~~~~~~~~~~~~~~~~~~
a4=a4-1+a4-3=4+2=6
a5=a5-1+a5-3=6+3=9
a6=a6-1+a6-3=9+4=13
a7=a7-1+a7-3=13+6=19
...and so on..
I think i did problem c. wrong but i'll post it here anyways:
c. a1=2, an+1=an!
~~~~~~~~~~~~~~~~~~~~~
a2=a1+1=a1!=2
a3=a2+1=a2!=2
... and so i got 2 for all of them..
I have another problem like this i'm having trouble with but i'd rather post it after i get this one over with. Thx in advance

i only examined c since you said you weren't sure about that. it's correct. you can post the next problem in a new thread

7. b looks ok too