SOLUTION: Forgive me for asking this again but I am having trouble understanding how to solve this problem. Please help me solve this problem: A certain arithmetic sequence has a_(base)5=

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Question 986769: Forgive me for asking this again but I am having trouble understanding how to solve this problem. Please help me solve this problem:
A certain arithmetic sequence has a_(base)5=-10 and a_(base)12=18 .
Find a_(base)2 and a_(base)17.
Thank you for your help and time.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You are told the values are part of an arithmetic sequence. That says that each "next value" in the sequence is one more step size different than the previous value in the sequence. You are given the 5th and 12th entries in the sequence
The 5th sequence value is -10
The 12th sequence value is 18
That says there are 7 steps (12-5) that result in a difference of 28 (18 - -10)
Thus each step is then 28/7 = 4 greater then the previous step
What is the value at 2?
2-5 = -3. -3 * 4 = -12. So the value at 2 is 12 less than the value at 5. -10-12 = -22
What is the value at 17? 17-12 = 5. 5*4 = 20. 18+20 = 38
you get the idea now?