x + x+6 +x+12+x+18+ x+24 = 930
5x + 90 = 930
5x = 930 - 60
5x = 870
x = 174 (which is the smallest consec multiple of 6)
174 is answer.
Given that sum of 5 consecutive multiples of 6 is 930
To find the smallest multiple
The consecutive multiples of 6 would be of the form
6(k-2), 6(k-1), 6k, 6(k+1), 6(k+2) for some natural number k.
The sum would be
6(k-2)+ 6(k-1)+ 6k+ 6(k+1)+ 6(k+2)= 6(5k) = 930
Divide by 30
k = 930/30 = 31
Smallest number = 6(k-2) = 6(31-2)
= 6(29) = 174
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Verify:
174+180+186+192+198 = 930
Hence verified
