Question

In a G.P., the fourth term is 48 and the eighth
term is 768. Find the tenth term.​

Answer 1

given : t4 = ar^3

:. ar^3 = 48 ----------1)

t8 = ar^7

:. ar^7 = 768 -----------2)

let ,. a , ar , ar^2 , ar^3 , ar^4 , ar^5 , ar^6 ,

ar^7 , ar^8 , ar^9

solution :

dividing equation 2) and 1)

ar^7 / ar^3 = 768 / 48

:. r^4 = 384 / 24 = 32 / 2 = 16

:. r^4 = 16

:. r = 2

putting r = 2 in eq. 1)

:. ar^3 = 48

:. a ( 2 ) ^ 3 = 48

:. a * 8 = 48

:. a = 48 / 8

:. a = 6

t10 = ar^9

:. t10 = 6 ( 2 ) ^ 9

:. t10 = 6 * 512

:. t10 = 3072