Question

If the 4th and 9th terms of a GP are 54 and 13122 respectively. Find the GP.
Also find its general term.​

Answer 1

Step-by-step explanation:

4th term = a r^3 = 54 ---->1

9th term = a r^ 8= 13122----->2

equation 2÷ equation 1

$\frac{a {r}^{8} }{a {r}^{3} } = \frac{13122}{54}$

${r}^{5} = 243 = {3}^{5}$

r=3

from 1

a r^3 = 54

=> a 3^3= 57

=>27a= 57

=> a= 57/27= 19/9

general term = ar^(n-1)

=( 19/9 )3^(n-1)

= 19/(3^2) (3^(n-1)

= 19× 3(n-3)

general term = 19× 3(n-3)