48,12,3,(3/4),...is a GP of form a,ar,ar^2,....,ar^(n-1),...where a is 1st term, r is the common ratio between consecutive terms {[t(n+1)/t(n)], n= 1,2,...

and t(n) = ar^(n-1). Here a = 48, r = (1/4) and t(n) = 48(1/4)^(n-1) =

3*(4^2)[4^(1-n)] = 3*4^(3-n). t(7) = 3*4^(3-7) = 3/(4^4) = 3/(2^8) = (3/256).

An = An-₁ / 4

A₁ = 48

A₂ = A₁/4 = 48/4 = 12

A₃ = A₂/4 = 124 = 3

A₄ = A₃/4 = ¾

A₅ = A₄/4 = (³/₄)/4 = ³/₁₆

A₆ = A₅/4 = (³/₁₆)/4 = ³/₆₄

A₇ = A₆/4 = (³/₆₄)/4 = ³/₂₅₆.......................ANS

geometric sequence

a₁ = 48

common ratio = ¼

nth term = a₁(¼)ⁿ⁻¹

a₇ = a₁(¼)⁶ = 48(¼)⁶ = 3/256

A[n] = 192/(4^n)

Plug in n=7

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