Q9 of 176 Page 21

The fourth term of a G.P. is 27, and the 7th term is 729, find the G.P.

T_n = ar^n-1

a =a, r =?, T_n = 27 n=4

a =a, r =?, T_n = 729 n=7

∴ 27 = a.r^4-1

⇒ 27 =a.r³…(1)

∴ 729 = a.r^7-1

⇒ 729 = a.r⁶…(2)

Divide (2) by (1) we get

⇒

⇒ r³ = 27

⇒ r = 3

Substituting r in 1 we get

a = 1

∴ GP = 1,3,9…

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