Question

what is sum of 7 consecutive odd integers?
Ms. Sue
Which integers?
If x = smallest integer,

x + (x+2) + (x+4)… + (x+12) = ?
sum of 1st 7 odds is 7^2 = 49
so, if you start with 2k+1 instead of 1, then each odd number is increased by 2k, so you wind up with 7*2k + 49

check: let k=5 and you have
11+13+15+17+19+21+23 = 119 = 7*10+49

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