Question: If A sub 8 equals 22 and S sub 8 equals 8, find A sub 10 of an arithmetic Sequence
We are given that A8 = 22, and S8 = 8.
In any arithmetic sequence, the nth term is given by,
An = A1 + (n-1)d (i.e. the 1st term plus (n-1) differences)
And the sum of the 1st n terms is given by
Sn = n(2*A1 + (n-1)d)/2
From the information given,
A8 = 22 = A1 + 7d
S8 = 8 = 8(2*A1 + 7d)/2
We thus have two equations in two unknowns, d and A1,
22 = A1 + 7d
2 = 2*A1 + 7d
Subtracting 1st eqn from 2nd eqn,
-20 = A1
i.e. A1 = -20
and d = 42/7 = 6
Then, An= A1 + (n-1)d = -20 + 6n - 6 = 6n - 26,
And A10 = 60 - 26 = 34
Answer: A10 = 34