Asked by jessica

in an arithmetic sequence 17th term is 9 times the first three terms and the 9th term is 6 less than 3 times the 1st term. Find the first three terms
Answered by Reiny
a+16d = 9(a + a+d + a+2d)
a+16d = 27a + 27d
-11d = 26a

a+8d = 3a - 6
8d+6 = 2a or
a = 4d+3 <----- sub that into the first equation
-11d = 26(4d+3)
-11d = 104d + 78
-115d = 78
d = -78/115
a = 4(-78/115) + 3 = 33/115

the first 3 terms are : 33/115 , -9/23, -123/115

check:
the sum of the first 3 is -27/23
9 times that sum = -243/23
17th term = -243/23 , check!

9th term = -591/115
3 times the first - 6 = -591/115 , check

I was expecting nicer numbers, but my answer works.



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