SOLUTION: let a<sub>n</sub> be an arithmetic sequence. if a<sub>4</sub>=27 and a<sub>9</sub>=67, what is a<sub>1</sub>?

Algebra ->  Sequences-and-series -> SOLUTION: let a<sub>n</sub> be an arithmetic sequence. if a<sub>4</sub>=27 and a<sub>9</sub>=67, what is a<sub>1</sub>?      Log On


   

Question 816667: let an be an arithmetic sequence. if a4=27 and a9=67, what is a1?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
let an be an arithmetic sequence. if a4=27 and a9=67, what is a1?
an = a1 + (n-1)d

a4 = a1 + (4-1)d
27 = a1 + 3d

a9 = a1 + (9-1)d
67 = a1 + 8d

So we solve this system of equations:

27 = a1 + 3d
67 = a1 + 8d

To eliminate d, multiply the first 
equation through by -8, and multiply
the second equation through by 3

-216 = -8a1 - 24d
 201 =  3a1 + 24d
-------------------
 -15 = -5a1
   3 = a1

--------------------

To check we find d by substituting
3 for a1 in

27 = a1 + 3d
27 = 3 + 3d
24 = 3d
 8 = d

So the sequence is found by starting with 
3 and adding 8 each time to get the next
term:

3, 11, 19, 27, 35, 43, 51, 59, 67

Edwin