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given the recursive sequence defined below, find the  first four terms.

a1=3

an=2an-1-n

 Jun 4, 2021

Best Answer 

 #1
avatar+179 
+2

a1 = 3

a2 = 2(a1)-2 = 6-2 = 4

a3 = 2(a2)-3 = 8-3 = 5

a4 = 2(a3)-4 = 10-4 = 6

 

 

 

Extra inductive proof to support the pattern shown above

 

By induction, if an= n+2, then

a(n+1)= 2(n+2)-(n+1)

           =n+3

which follows the inductive assumption. 

 

With the base case of a1 and a2, this hence proves that an=n+2.

 Jun 4, 2021
 #1
avatar+179 
+2
Best Answer

a1 = 3

a2 = 2(a1)-2 = 6-2 = 4

a3 = 2(a2)-3 = 8-3 = 5

a4 = 2(a3)-4 = 10-4 = 6

 

 

 

Extra inductive proof to support the pattern shown above

 

By induction, if an= n+2, then

a(n+1)= 2(n+2)-(n+1)

           =n+3

which follows the inductive assumption. 

 

With the base case of a1 and a2, this hence proves that an=n+2.

EnchantedLava68 Jun 4, 2021
 #2
avatar+121054 
+1

Very nice, EnchantedLava   !!!!

 

 

cool cool cool

 Jun 4, 2021
 #3
avatar+179 
0

Thanks!

EnchantedLava68  Jun 4, 2021

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