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If for a G.P., Tn = 324, Sn = 484 and r = 3; find a and n.

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Tn = 324, Sn = 484, r = 3, a =?, n =?

Now, Sn = \(\frac{rT _n−a}{r−1}\)

∴ 484 = \(\frac{3(324)−a}{3−1}\)

∴ 484 = \(\frac{972−a}{2}\)

∴ 484 × 2 = 972 – a

∴ a = 972 – 968

a = 4

Now, Tn = a.rn-1

∴ 324 = 4(3)n-1

∴ 324 / 4 = (3)n-1

∴ (3)4 = (3)n-1

∴ 4 = n – 1 ( Base are equal, Index are also equal)

∴ n = 5

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