SOLUTION: The seventh term of an arithmetic sequence is 1/2 and the 14th term is 6. What is the tenth term?

Question 1044781: The seventh term of an arithmetic sequence is 1/2 and the 14th term is 6. What is the tenth term?
Found 2 solutions by Cromlix, advanced_Learner:
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
The seventh term of an arithmetic sequence is 1/2.
1/2 =a1 + (7 - 1)d
The 14th term is 6
6 = a1 + (14 - 1)d
...............
1/2 = a1 + 6d......(1)
6 = a1 + 13d.......(2)
Subtract Eq(1) from Eq(2)
11/2 = 7d
d = 11/14.
Substitute d = 11/14 into Eq(1)
1/2 = a1 + 6d......(1)
1/2 = a1 + 6(11/14)
1/2 =a1 + 66/14
a1 = 1/2 - 66/14
a1 = -59/14
.........
Tenth term =
a1 + (10-1)d
-59/14 + 9(11/14)
-59/14 + 99/14
= 40/14 = 20/7
Hope this helps :-)
Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
.

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