Asked by Nancy

what is the first term of an arithmetic sequence if the 7th term is 21 and the 10th term is 126
Answered by MathMate
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) = 126-21
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)=21-245=-224

T(n) = -224 + 35n
Answered by Reiny
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<sub>7</sub> = -189 + 6(35) = 21
t<sub>10</sub> = -189 + 9(35) = 126
There are no AI answers yet. The ability to request AI answers is coming soon!