SOLUTION: A certain arithmetic sequence has a_(base)5=-10 and a_(base)12=18 . Find a_(base)2 and a_(base)17. Thank you

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Question 986764: A certain arithmetic sequence has a_(base)5=-10 and a_(base)12=18 .
Find a_(base)2 and a_(base)17.

Thank you
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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A certain arithmetic sequence has  a%5B5%5D = -10  and  a%5B12%5D = 18.  Find  a%5B2%5D  and  a%5B17%5D.
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According to the condition,

a%5B5%5D = a%5B1%5D + %285-1%29%2Ad = a%5B1%5D + 4%2Ad = -10           (1)     and

a%5B12%5D = a%5B1%5D + %2812-1%29%2Ad = a%5B1%5D + 11%2Ad = 18.       (2)

By distracting (1) from (2) you get

(11 - 4)*d = 18 - (-10),

7d = 28.

Hence,  d = 28%2F7 = 4  (the common difference of the arithmetic progression).

Now from  (1)  you will easily find  a%5B1%5D = -10 - 4*4 = -26.

From this point,  complete yourself the remaining part.