<PRE><B>Question 1142569</B>
The formula for the nth term of an arithmetic sequence is
:
x(n) = a +d(n-1), where is the first term, d is the common difference
:
x(7) = 1/2 = a +d(7-1)
:
1) a +6d = 1/2
:
x(14) = 6 = a +d(14-1)
:
2) a +13d = 6
:
equation 1, multiply both sides of = by 2
:
3) 2a +12d = 1
:
solve equation 2 for a
:
a = 6 -13d
:
substitute for a in equation 3
:
2(6-13d) +12d  = 1
:
12 -26d +12d = 1
:
-14d = -11
:
d = 11/14
:
a = 6 -13(11/14)
:
a = 84/14 -143/14 = -59/14
:
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x(10) = -59/15 +11/14(9) = 40/14 = 20/7
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