Question

if the fourth and seventh term of gp are 24 and 192 find the fifth term .​

Answer 1

Step-by-step explanation:

$a {r}^{3} = 24...................(1)$

$a {r}^{6} = 192....................(2)$

$(2) \div (1)$

$\frac{a {r}^{6} }{a {r}^{3} } = \frac{192}{24}$

${r}^{3} = 8$

$r = 2$

$a {2}^{3} = 24$

$a = \frac{24}{8} = 3$

$the \: fifth \: \: element \: gp = a {r}^{4} = 3. {2}^{4} = 3.16 = 48$