Question

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

Answer 1

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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