SOLUTION: the 7th term of an arithmetic sequence is 1/2 and the 14th term is 6 what is the 10th term?

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Question 1142569: the 7th term of an arithmetic sequence is 1/2 and the 14th term is
6 what is the 10th term?
Found 3 solutions by rothauserc, Edwin McCravy, josmiceli:
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
:
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
:
******************************************
x(10) = -59/15 +11/14(9) = 40/14 = 20/7
******************************************
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

__,__,__,__,__,__,1/2,__,__,??,__,__,__,__,__, 6,__,...














So we have the system:



Solve for a1 in one of the equations and
substitute in the other to find d.  Then find d by 
substituting in the equation you got when you solved 
for d.  Then substitute the values n=10, along with 
what you got for a1 and d.


Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

= the difference between successive terms
= the number of the term
= the first term
------------------------------

(1)
------------------------------

(2)
------------------------------
subtract (1) from (2)
(2)
(1)
---------------------------


and
(2)
(2)
(2)
----------------------------------




-----------------------------
check answer:
What is the 7th term?




What is the 14th term?




OK
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