The first two terms of a geometric progression add up to $12.$ the sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative, then the first term is

  • [AIEEE 2008]
  • A

    $-4$

  • B

    $-12$

  • C

    $12$

  • D

    $4$

Similar Questions

If $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then

  • [IIT 1966]

The first and last terms of a $G.P.$ are $a$ and $l$ respectively; $r$ being its common ratio; then the number of terms in this $G.P.$ is

If $2^{10}+2^{9} \cdot 3^{1}+28 \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}=S -211$ then $S$ is equal to

  • [JEE MAIN 2020]

Find the sum to $n$ terms of the sequence, $8,88,888,8888 \ldots$

Find the $20^{\text {th }}$ and $n^{\text {th }}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$