# Thread: How to find the first 5 terms of an arithmetic sequence

1. ## How to find the first 5 terms of an arithmetic sequence

Hi all, I thought I was beginning to understand AP's but this problem has got me beat. if you are given only the first term u1 and then that un = un+1 - some number, how do you find the first 5 terms?

2. ## Re: How to find the first 5 terms of an arithmetic sequence

Please check if you have copied the question correctly. As I understand you are given the first term. Let first term = a
n th trm = (n+2)th term - k ( suppose) Then it is quite simple and you get
a + ( n-1) d = a + nd - k That gives d, common difference d = k Now you can work out the solution

3. ## Re: How to find the first 5 terms of an arithmetic sequence

If you let some number be d, then you can write the recursion as:

$\displaystyle u_{n+1}=u_{n}+d$

This means:

$\displaystyle u_2=u_1+d$

$\displaystyle u_3=u_2+d=u_1+2d$

Do you see the pattern?

4. ## Re: How to find the first 5 terms of an arithmetic sequence

So if I wanted the 5th term it would be u5 = U1 + 5d?

5. ## Re: How to find the first 5 terms of an arithmetic sequence

No, look at the pattern:

$\displaystyle u_1=u_1+0\cdot d=u_1+(1-1)d$

$\displaystyle u_2=u_1+1\cdot d=u_1+(2-1)d$

$\displaystyle u_3=u_1+2\cdot d=u_1+(3-1)d$

Do you see the pattern that will continue? Can you state what the general term $\displaystyle u_n$ is?

6. ## Re: How to find the first 5 terms of an arithmetic sequence

Ok so have I done this right? I was given that u1 = 5 and un+1 = un-2.3 and asked to find the first 5 terms, so I used the formula un = a+(n-1)d. I took a = 5 and d = -2.3 and here is what I came up with;
u1 = 5 + (1-1)-2.3 = 2.7
u2 = 5+ (2-1)-2.3 = 2.7
u3 = 5+ (3-1)-2.3 = 0.4
u4 = 5+ (4-1)-2.3 = -1.9
u5 = 5+(4-1)-2.3 = -4.2

The difference is -2.3 in the last 4, so I assume I am correct? But u1 and u2 should not have the same value?