Given that 1^{2}+2^{2}+3^{2}+\ldots+10^{2}=385, what is the value of 3^{2}+6^{2}+9^{2}+\ldots+30^{2} ?

GMAT Exponents Explained — Given that 1^{2}+2^{2}+3^{2}+\ldots+10^{2}=385, what is the value of...

Given that 1^{2} + 2^{2} + 3^{2} + \dots + 1 0^{2} = 385, what is the value of 3^{2} + 6^{2} + 9^{2} + \dots + 3 0^{2} ?

exponentssequences & seriesfactoring

Explanation	Calculations	Help
$We first name the sum we want to find.$	$S = 3^{2} + 6^{2} + ... + 3 0^{2}$
$We then note that each term can be written as (3 k)^{2} where k runs from 1 to 10.$	$S = (3 \times 1)^{2} + (3 \times 2)^{2} + ... + (3 \times 10)^{2}$
$We then factor out the common factor 9 from each squared term.$	$S = 9 \times (1^{2} + 2^{2} + ... + 1 0^{2})$
$We then substitute the given value and multiply.$	$S = 9 \times 385 = 9 \times (400 - 15) = 9 \times 400 - 9 \times 15 = 3600 - 135 = 3465$	Theory & Tactics Method Card CALC2-D Click to view full details

Scroll horizontally to view all columns

3465