Question 1066076: Find the missing terms of the arithmetic sequence...
27, ?, ?, ?, 53,...
Show each step of the process clearly.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The formula for the nth term of an arithmetic sequence is
:
a(n) = a(1) +d(n-1) where a(1) is the first term and d is the common difference
:
we have two formulas in two unknowns
:
1) 27 = a(1) +d(1-1)
2) 53 = a(1) +d((5-1)
:
from equation 1), we have a(1) = 27
:
substitute 27 for a(1) in equation 2
:
53 = 27 +4d
:
4d = 26
:
d = 6.5
:
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a(2) = 27 +6.5(2-1) = 33.5
a(3) = 27 +6.5(3-1) = 40
a(4) = 27 +6.5(4-1) = 46.5
:
completed sequence is
:
27, 33.5, 40, 46.5, 53
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