Question

In a GP the tenth term is 9 and fourth term is 4 then its seventh term is ?​

Answer 1

Answer:

A10=9

A4=4

d=am-an/m-n

d=9-4/10-4

d=5/6

Answer 2

SoluTion :-

$\sf {General\ term\ of\ G.P=ar^{n-1}}\\\\\\\\\sf {Given :}\\\\\sf {a10=9}\\\\\sf {a4=4 }\\\\\\\sf {\Rightarrow\ ar^{9}=9\ and\ ar^{3}=4 }$

On dividing we get,

$\sf {\frac{ar^{9}}{ar^{3}} =\frac{9}{4} \Rightarrow r^{6}=\frac{9}{4} }\\\\\\\\\\sf {ar^{3}=4 \Rightarrow (ar^{3})^{2}=16 }\\\\\\\\\sf {=a^{2}r^{6}=16 }\\\\\\\\\sf {=a^{2} \times \frac{9}{4}=16 }\\\\\\\sf {=a^{2}=\frac{64}{9} }\\\\\\\sf {=a=\frac{8}{3} }\\\\\\\\\sf {\therefore a_{7}=ar^{6}=\frac{8}{3} \times \frac{9}{4}=6}$