+0  
 
0
6
1
avatar+952 

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence.  If a_1 + a_3 + a_5 = 7 and a_2 + a_4 = 6, then find a_1.

 Apr 9, 2024
 #1
avatar+128794 
+1

a1 + a3 + a5  =  7

a1 + (a1 + 2d) +( a1 + 4d)  =  7

3a1 + 6d  = 7

 

a2 + a4  = 6

(a1 + d)   + ( a1 + 3d )  =  6

2a1 + 4d  = 6

 

3a1 + 6d   =  7    mult through by 4

2a1 + 4d = 6      mult through by -6

 

12a1 + 24d  = 28

-12a1 - 24d  = -36         adding these we get

 

0  =  -  8

 

No solution

 

cool cool cool

 Apr 9, 2024

2 Online Users

avatar