SOLUTION: what is the sum of the integers between 20 and 480 that are multiples of 11? please use the equation needed, thank you:)

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Question 275375: what is the sum of the integers between 20 and 480 that are multiples of 11?
please use the equation needed, thank you:)
Found 2 solutions by user_dude2008, Edwin McCravy:
Answer by user_dude2008(1862)   (Show Source): You can put this solution on YOUR website!
22+33+44+...+451+462+473 = 11(2+3+4+...+41+42+43)


11(2+3+4+...+41+42+43) = 11(1+2+3+4+...+41+42+43-1)

11(2+3+4+...+41+42+43) = 11((43(43+1))/2-1)

11(2+3+4+...+41+42+43) = 11(946-1)

11(2+3+4+...+41+42+43) = 11(945)

11(2+3+4+...+41+42+43) = 10395


Answer: 22+33+44+...+451+462+473 = 10395
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
what is the sum of the integers between 20 and 480 that are multiples of 11?
please use the equation needed, thank you:)

The first term is 22 and we can find the last term by dividing

 by , getting  So  or  is the
last term.

The multiples of  are  apart, so we have an arithmetic
sequence for which the common difference,  is .

The formula for the sum which we need is this:



where  is the first term and  is the last
term.



But we need , so we first need the formula for the nth term:















No we can substitute 



where ,  and  







Edwin
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