If A sub 8 equals 22 and S sub 8 equals 8, find A sub 10 of an arithmetic Sequence

Question

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Answer 1

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Answer 2

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