Given that 1^{2} + 2^{2} + 3^{2} + \ldots + 8^{2} = 204, what is the value of 4^{2} + 8^{2} + 12^{2} + \ldots + 32^{2}?

Given that 1^{2} + 2^{2} + 3^{2} + \ldots + 8^{2} ... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Algebra (Exponents)

Given that 1^{2} + 2^{2} + 3^{2} + \dots + 8^{2} = 204, what is the value of 4^{2} + 8^{2} + 1 2^{2} + \dots + 3 2^{2} ?

Explanation	Calculations	Help
$We first write the sum we want to find.$	$S = 4^{2} + 8^{2} + 1 2^{2} + ... + 3 2^{2}$
$We observe that each term is of the form (4 k)^{2} for k from 1 to 8.$	$S = (4 \times 1)^{2} + (4 \times 2)^{2} + ... + (4 \times 8)^{2}$
$We factor out 16 from each term.$	$S = 16 \times (1^{2} + 2^{2} + ... + 8^{2})$
$We substitute the given value and break the multiplication into simpler parts.$	$S = 16 \times 204 = 16 \times (200 + 4) = 16 \times 200 + 16 \times 4 = 3200 + 64 = 3264$	Theory & Tactics Method Card CALC2-D Click to view full details

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B

GMAT Quant — Algebra (Exponents)

Given that 1^{2} + 2^{2} + 3^{2} + \dots + 8^{2} = 204, what is the value of 4^{2} + 8^{2} + 1 2^{2} + \dots + 3 2^{2} ?

Explanation	Calculations	Help
$We first write the sum we want to find.$	$S = 4^{2} + 8^{2} + 1 2^{2} + ... + 3 2^{2}$
$We observe that each term is of the form (4 k)^{2} for k from 1 to 8.$	$S = (4 \times 1)^{2} + (4 \times 2)^{2} + ... + (4 \times 8)^{2}$
$We factor out 16 from each term.$	$S = 16 \times (1^{2} + 2^{2} + ... + 8^{2})$
$We substitute the given value and break the multiplication into simpler parts.$	$S = 16 \times 204 = 16 \times (200 + 4) = 16 \times 200 + 16 \times 4 = 3200 + 64 = 3264$	Theory & Tactics Method Card CALC2-D Click to view full details

Scroll horizontally to view all columns

B