Question

Find the 10th term and the general term of the progression
`1/4, (-1)/2, 1, -2, 4`, ...

Answer 1

In the given progression, we have
`((-1)/2) div 1/4 =((-1)/2xx4)=-2, 1 div ((-1)/2)=1xx(-2)=-2`,
`(-2) div 1=-2` and `4 div (-2)=-2`.
So, the given progression is a GP in which `a=1/4` and `r=-2`.
`:.` the 10th term, `T_(10)=a r^((10-1))=ar ^(9)=1/4 xx (-2)^(9)=(-512)/4=-128`.
The general term, `T_(n)=ar^((n-1))=1/4xx(-2)^((n-1))=(-1)^((n-1))xx2^((n-3))`.