Find the sum of all the multiples of 5 between 312 and 463 using an arithmetic progression formula ?

1 Answer
Jan 4, 2018

Sum of all multiples of #5# between #312 and 463# is #11625#

Explanation:

First term of A.P is #a_1=315# and last term of A.P is #a_n=460#

Common difference is #d=5# . We know #a_n=a_1+(n-1)d#

#:. 460=315+(n-1)*5 or n-1= (460-315)/5=29#

#:. n=30 :. # Number of terms in A.P is #n=30#

Mid term is mean of first term and last term.

#a_m=(315+460)/2= 387.5 #

Sum #S_n = a_m*n= 387.5 *30 = 11625#

Sum of all multiples of #5# between #312 and 463# is #11625#

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