Given data :
a₃ = 9/16
aₓ = -3/4 · aₓ₋₁
Where x is the number of terms ('x' is also written as 'n')
To find the 7th term (a₇):
We know that aₓ = -3/4 · aₓ₋₁
So,
a₃ = -3/4 · a₃₋₁
a₃ = -3/4 · a₂
9/16 = -3/4 · a₂
a₂ = 9/16 × -4/3
a₂ = -36/48
a₂ = -3/4
Again,
aₓ = -3/4 · aₓ₋₁
a₄ = -3/4 · a₄₋₁
a₄ = -3/4 · a₃
a₄ = -3/4 · 9/16
a₄ = -27/64
a₄ = -27/64
For a₅,
aₓ = -3/4 · aₓ₋₁
a₅ = -3/4 · a₅₋₁
a₅ = -3/4 · a₄
a₅ = -3/4 × -27/64
a₅ = 81/256
For a₆,
aₓ = -3/4 · aₓ₋₁
a₆ = -3/4 · a₆₋₁
a₆ = -3/4 · a₅
a₆ = -3/4 × 81/256
a₆ = -243/1024
For a₇,
aₓ = -3/4 · aₓ₋₁
a₇ = -3/4 · a₇₋₁
a₇ = -3/4 · a₆
a₇ = -3/4 × -243/1024
a₇ = 729/4096
One gallon is equivalent to 128 fluid ounces
3 gallons is equivalent to 3*128 fluid ounces
= 384 fluid ounces
One plastic cup can hold 12 guide ounces
So cups needed will be 384/12
32 cups
the answer would be revenue
