Question

Find the eighth term of the following geometric sequence 14,-7, 7/2

Answer 1

You can see that you get the next term by dividing by 2 and switching sign (that is, dividing by -2).

So, the general term is

`a_n = (14)/((-2)^(n-1))`

In fact, you can check that

`a_1 = (14)/((-2)^0)=(14)/(1)=14`

`a_2=(14)/((-2)^1)=(14)/(-2)=-7`

`a_3=(14)/((-2)^2)=(14)/(4)=(7)/(2)`

So, the eight term is

`a_8=(14)/((-2)^7)=(7)/(-2^6)=-(7)/(64)`

Answer 2

7/32
Keep the pattern going. A(n)=A(n-1)*-1/2
14, -7, 7/2, -7/4, 7/8, -7/16, 7/32