SOLUTION: Find the explicit forumla for th following sequence: a5= -17 and a28= 374

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Question 805263: Find the explicit forumla for th following sequence:
a5= -17 and a28= 374
Answer by waynest(281) About Me  (Show Source):
You can put this solution on YOUR website!
-17 = a + (5-1)d 374 = a + (28 - 1)d
-17 = a + 4d 374 = a + 27d
subtract equation 1 from equation 2
374 = a + 27d
-(-17 = a + 4d)
391 = 23d
391/23 23d/23
17 = d
substitute 17 for d in equation 1
-17 = a + (5 - 1 )17
-17 = a + 68
-17 - 68 = a + 68 - 68
-85 = a
substitute both into equation 1 to get the explicit formula
t(n) = -85 + (n - 1)17
t(n) = -85 + 17n - 17
t(n) = 17n - 102
check:
t(5) = 17(5) - 102
t(5) = 86 - 102
t(5) = -17
t(28) = 17(28) - 102
t(28) = 476 - 102
t(28) = 374