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Let a1, a2, a3, ..., a10, a11, a12 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.

 Mar 13, 2024
 #1
avatar+818 
0

 

Let a1, a2, a3, ..., a10, a11, a12 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.  

 

                                                         a1 + a2 = 4   &   a2 + a3 = 5  

 

Since it's an arithmetic sequence, the difference between adjacent terms is the same.  

 

Call that difference, i.e., the increment, let's call it "n".  Just keep this in mind for a while.  

 

                                                         a2 + a3 = 5    

                                                         a1 + a2 = 4    

Subtract one from the other  

                                                         a3 – a1 = 1  

Since a3 is (a1 + n + n)  

                                                         (a1 + n + n) – a1 = 1  

 

                                                          2n = 1  therefore n = 0.5  

Referring back to the top   

                                                          a1 + a2 = 4  

a2 = (a1 + 0.5) so plug it in  

                                                           a1 + (a1 + 0.5) = 4  

 

                                                           2a1 + 0.5 = 4  

 

                                                           2a1 = 4 – 0.5 = 3.5    

 

                                                            a1 = 3.5 / 2  

 

                                                            a1 = 1.75   

check answer  

                                                            a1 = 1.75  

                                                            a2 = 2.25        a1 + a2 = 4  

                                                            a3 = 2.75        a2 + a3 = 5 

.

 Mar 14, 2024
 #3
avatar+16 
-1

"Liliam0216" is a bot and therefore will not be able to figure out which two of your generally unecessary steps are not needed.

 Mar 15, 2024
edited by Holtran  Mar 15, 2024

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