Posted by Nancy on Saturday, February 13, 2010 at 10:55pm.
what is the first term of an arithmetic sequence if the 7th term is 21 and the 10th term is 126

Math/Precal  MathMate, Saturday, February 13, 2010 at 11:23pm
For an arithmetic sequence, the nth term is given by:
T(n)=T(0)+kn,
where k is a constant.
Knowing T(7)=21, and T(10)=126
we find k using
T(10)T(7) = 12621
T(0)+10k  (T(0)+7k) = 105
3k = 105
k=35
From the value of k, we find T(0):
T(n)=T(0)+35n
T(7)=T(0)+35(7) = 21
T(0)=21245=224
T(n) = 224 + 35n

Math/Precal  Reiny, Saturday, February 13, 2010 at 11:35pm
7th term is 21 > a+6d = 21
10th term is 126 > a + 9d = 126
subtract them:
3d = 105
d = 35
back in a+6d = 21 > a = 189
first term is 189
check:
t_{7} = 189 + 6(35) = 21
t_{10} = 189 + 9(35) = 126
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