SOLUTION: arithmetic sequence a10=x+3 a11=2x+7 a12=4x-2 which term equals 186

Question 265723: arithmetic sequence a10=x+3 a11=2x+7 a12=4x-2 which term equals 186
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We know the following:
a10 = x+ 3
a11 = 2x+7
a12 = 4x-2
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since this is arithmetic all differences are "common" or the same
a11 - a10: x+4
a12 - a11: 2x - 9
set these equal and solve for x to get
x+ 4 = 2x - 9
subtract x to get
4 = x - 9
add 9 to get
x = 13
now we see that
a10 = 13 + 3 =16
a11 = 2*13 + 7 = 33
a12 = 4*13 - 2 = 50
the common difference is 17 and the tn formula is
Tn = 17n - 154
Now we want the nth term at 186 so we get
186 = 17n - 154
add 154 to get
17n = 340
n = 20
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