I suppose you just have to simplify this expression.
(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)
Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :
… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)
Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have
… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)
… = (2¹ - 2²) / (2⁰ - 2¹)
… = (2 - 4) / (1 - 2)
… = (-2) / (-1)
… = 2
Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :
… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)
… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)
… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)
… = (-4<em>y</em>) / (-2<em>y</em>)
… = 2
Answer:
1.88 pounds
Step-by-step explanation:
First, find the total amount of sugar, since there were 2 shipments
22.56(2)
= 45.12
Then, divide this by 24:
45.12/24
= 1.88
So, each canister had 1.88 pounds of sugar
= 1455
generate a few terms of the sequence using 
= 3n + 2
= ( 3 × 1) + 2 = 5
= (3 × 2) + 2 = 8
= (3 × 3 ) + 2 = 11
= (3 × 4 ) + 2 = 14
= ( 3 × 5 ) + 2 = 17
the terms are 5, 8, 11, 14, 17
these are the terms of an arithmetic sequence
sum to n terms is calculated using 
= 
[ 2a + (n-1)d]
where a is the first term and d the common difference
d = 8 - 5 = 11 - 8 = 14 - 11 = 3 and = 5
= 
[( 2 × 5) + (29 × 3) ]
= 15( 10 + 87) = 15 × 97 = 1455
