Question 935889: The seventh term of arithmetic progression series is 29 and the eleventh term is 54. Determine the sixteenth term.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! arithmetic progression series is defined by the following formula,
Xn = X1 + d*(n-1) where n is the nth term, X1 is the first term, d is common difference between terms. The problem gives us two formulas
X7 = X1 + d*(7-1) = 29
X11 = X1 + d*(11-1) = 54
combine like terms in both equations
X1 + 6d = 29
X1 + 10d = 54
subtract equation 1 from equation 2
4d = 25
d = 6.25
substitute for d in first equation
X1 + 6*6.25 = 29
X1 = 29 - 37.5 = -8.5
now calculate the 16th term
X16 = -8.5 + 6.25 * (16-1) = 85.25
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