There is a sequence of numbers such that every entry except for the first entry is the arithmetic mean of its two neighboring entries. The 27th entry is 94 and the 94th entry is 46. What's the first entry?
Using the formula: tn = t1 + (n - 1)d
94 = t1 + (27 - 1)d 46 = t1 + (94 - 1)d
94 = t1 + 26d 46 = t1 + 93d
Combining these two formulas:
94 = t1 + 26d
46 = t1 + 93d
Subtracting down:
48 = - 67d ---> d = -48/67 and t1 = 112 42/67
