Question

Find a Geometric Progression for which the sum of first two terms is -4 and the fifth term is 4 times the third term.
(2 marks)

Answer 1

Let ‘a’ be the first term and ‘r’ be the common ratio of the given Geometric Progression.

Then, according to the problem the sum of first two terms is -4

$t_1+t_2=-4$

$a+ar=-4$ .................. (i)

and the fifth term is 4 times the third term. ( 1 mark)
$t_5=4\times t_3$
$a{r}^4=4\times a{r}^2$
$r^2=4$
$r=\pm 2$

Putting r = 2 and -2 respectively in (i), we get a = -4/3 and a = 4.

Thus, the required Geometric Progression is -4/3, -8/3, -16/3, ............ or 4, -8, 16, -32, ........................ ( 1 mark)