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In an arithmetic sequence a1, a2, a3, . . . , we know a1 = 1 and an = 1/n for some integer n > 1.

(a) What is the common difference of this arithmetic sequence, in terms of n?

(b) Compute the value of an+1.

 Feb 22, 2021
 #1
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+1

We  have

 

1 , 1/2, 1/3, 1/4 ,  etc

 

a)   the  common difference  is         1/ (n + 1)  -   1/n  =   (n - (n +1)) /  (n* (n+1))  = 

 

-1 / (n(n+1))

 

b)  an+ 1 =    1/n -  1 / (n(n+1)) =    (n + 1  - 1)/ (n (n + 1))  =      n / (n (n +1)) =   1/ (n +1)  

 

 

cool cool cool

 Feb 22, 2021

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