find G.P whose 4th term is 54 and the 7th term is 1458
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4th term = 54
7th term = 1458
t₄ = 54
a r³ = 54 ----- (1)
t₇ = 1458
a r⁶ = 1458 ----- (2)
(2)/(1) = (a r⁶)/(a r³) = 1458/54
r³ = 27
r³ = 3³
r = 3
Substitute r = 3 in the first equation we get
a (3)³ = 54
a(27) = 54
a = 54/27
a = 2
The general form of G.P is a, a r , a r ²,.........
= 2 ,2(3),2(3)²,..............
= 2,6,18,............
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