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 u_{1}and then that u_{n}= u_{n+1}-some number, how do you find the first 5 terms?

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- Apr 19th 2013, 02:46 AMalexpasty2013How 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 u

_{1}and then that u_{n}= u_{n+1}-*some number*, how do you find the first 5 terms? - Apr 19th 2013, 02:59 AMibduttRe: 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 - Apr 19th 2013, 03:02 AMMarkFLRe: 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? - Apr 19th 2013, 03:13 AMalexpasty2013Re: How to find the first 5 terms of an arithmetic sequence
So if I wanted the 5th term it would be u

_{5}= U_{1}+ 5d? - Apr 19th 2013, 03:26 AMMarkFLRe: 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? - Apr 22nd 2013, 01:11 AMalexpasty2013Re: How to find the first 5 terms of an arithmetic sequence
Ok so have I done this right? I was given that u

_{1}= 5 and u_{n}+1 = un-2.3 and asked to find the first 5 terms, so I used the formula u_{n}= a+(n-1)d. I took a = 5 and d = -2.3 and here is what I came up with;

u_{1}= 5 + (1-1)-2.3 = 2.7

u_{2}= 5+ (2-1)-2.3 = 2.7

u_{3}= 5+ (3-1)-2.3 = 0.4

u_{4}= 5+ (4-1)-2.3 = -1.9

u_{5}= 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?