Question

find the G.P where 4th term is 8 and 8th term is 128/625

Answer 1

Given, T4= 8=> ar³= 8
T8= 128/625=> ar^7= 128/625

T8/T4= 128/625 x 1/8
=> ar^7/ar³= 16/625
=> r^4= 2^4/5^4
=> r= 2/5

ar³= 8
=> a(2/5)³= 8
=> a x 8/125= 8
=> a= 125

Therefore, a= 125, ar= 125 x 2/5 = 50, ar²= 125 x 4/25 =20....
or 125, 50, 20, 8,... forms a G.P.

Answer 2

answer :

125, 50, 20, 8, 16/5, 32/25

Step-by-step explanation:

we have, r = ⅖ and a = 125

a, ar, ar², ar³, ar⁴, ar⁵, ar⁶, ar⁷, ar⁸.....

a = 125

ar = 50

ar² = 125 × (2/5)² = 20

ar³ = 125 × (2/5)³ = 8

ar⁴ = 125 × (2/5)⁴ = 16/5

ar⁵ = 125 × (2/5)⁵ = 32/25

and, so on..

finally the G.P is.. 125, 50, 20, 8, 16/5, 32/25

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