The first term of a geometric progression is $270$ and the fourth term is $80$. Find the common ratio.

The first term of a geometric progression is $50$ and the second term is $-30$. Find the fourth term.

The second term of a geometric progression is $12$ and the fourth term is $27$ . Given that all the terms are positive, find the common ratio and the first term.

The sum of the second and third terms in a geometric progression is $30$ . The second term is $9$ less than the first term. Given that all the terms in the progression are positive, find the first term.

Three consecutive terms of a geometric progression are $x,4\text{ and }x+6$. Find the possible values of $x$.

Find the sum of the first eight terms of the following geometric series,

$3+6+12+24+\cdots$

Find the sum of the first eight terms of the following geometric series,

$128+64+32+16+\cdots$

Find the sum of the first eight terms of the following geometric series,

$1-2+4-8+\cdots$

Find the sum of the first eight terms of the following geometric series,

$243+162+108+72+\cdots$