Question

If the average of 12 consecutive odd integers is 328, what is the least of these integers?

Answer 1

k + (k+2) + (k+4)... = 328

Answer 2

Figured it out! Yayy, but sort of really manually. Here's what I do:

12 consecutive odd numbers right? and 328 is the average. so 325 and 327 are going to be the mid values. I count back 5 odd numbers from 325 that is 317! and voila that's teh correct answer! If anyone knows any other quick solution or formula thingy let me know please!

Answer 3

That's the best way actually, and if I were in your place, would have done the same thing (I don't remember formulae that well)

But if you do need a formula, here's what we can do:

Let the first (and the least) odd no. be 2n+1 ...(since 2n+1is always odd)
So, the next 11 will be --> (2n+3, 2n+5, 2n+7,....2n+23)
all the 12 sum up 24n+144
now,

24n+144
------- = 328
12

or, 24n+144 = 12*328 = 3936
or, n = 3792/24 =158

so, the first odd no. = 2n+1 = 317


Same answer, albeit through a longer, time-consuming and rote process. But comes in handy just in case your brain isn't working.