Given that $1^{2}+2^{2}+...+12^{2}=650$, what is t... | Free GMAT Practice Question | GMAT Panda

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Given that 1^{2} + 2^{2} + ... + 1 2^{2} = 650, what is the value of 2^{2} + 4^{2} + ... + 2 4^{2} ?

Explanation	Calculations	Help
$We first name the sum we want to find.$	$S = 2^{2} + 4^{2} + ... + 2 4^{2}$
$We note that each term can be written as (2 k)^{2} where k runs from 1 to 12.$	$S = (2 \times 1)^{2} + (2 \times 2)^{2} + ... + (2 \times 12)^{2}$
$We then factor out the common factor 4 from each squared term.$	$S = 4 \times (1^{2} + 2^{2} + ... + 1 2^{2})$
$We substitute the given value and break down the multiplication.$	$S = 4 \times 650 = 4 \times (600 + 50) = 4 \times 600 + 4 \times 50 = 2400 + 200 = 2600$	Theory & Tactics Method Card CALC2-D Click to view full details

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B

Given that 1^{2} + 2^{2} + ... + 1 2^{2} = 650, what is the value of 2^{2} + 4^{2} + ... + 2 4^{2} ?

Explanation	Calculations	Help
$We first name the sum we want to find.$	$S = 2^{2} + 4^{2} + ... + 2 4^{2}$
$We note that each term can be written as (2 k)^{2} where k runs from 1 to 12.$	$S = (2 \times 1)^{2} + (2 \times 2)^{2} + ... + (2 \times 12)^{2}$
$We then factor out the common factor 4 from each squared term.$	$S = 4 \times (1^{2} + 2^{2} + ... + 1 2^{2})$
$We substitute the given value and break down the multiplication.$	$S = 4 \times 650 = 4 \times (600 + 50) = 4 \times 600 + 4 \times 50 = 2400 + 200 = 2600$	Theory & Tactics Method Card CALC2-D Click to view full details

Scroll horizontally to view all columns

B