SOLUTION: Find the smallest positive term of the progression 100, 97, 94...(Don't enumerate)

Question 1023578: Find the smallest positive term of the progression 100, 97, 94...(Don't enumerate)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i would find the number of terms required for the sum to be 0.
it will either be an integer, or it will not.
the answer will be 1 less than the number of terms indicated.

let's see if this works.

the general formula is An = A1 + (n-1) * d

since is equal to -3, and A1 is equal to 100, then the formula becomes An = 100 + (n-1) * -3.

simplify this to get An = 100 - 3 * (n-1).

simplify further to get An = 100 - 3n + 3.

simplify further to get An = 103 - 3n.

set An equal to 0 and this becomes 0 = 103 - 3n.

add 3n to both sides of this equation and you get 3n = 103.

divide both sides of this equation by 3 to get n = 103 / 3 = 34.333.....

take the lower figure and you get n = 34.

your answer should be that the smallest positive will be when n = 34.

when n = 34, the formula becomes An = 103 - 3 * 34 which is equal to 1.

when n = 35, the formula becomes An = 103 - 3 * 35 which is equal to -2.

looks like n = 34 gets you the least positive value which is 1.

sticking to the original formula, you would get:

An = 100 + (n-1) * -3 becomes An = 100 -3 * (n-1) which becomes A34 = 100 - 3 * 33 which becomes A34 = 100 - 99 which becomes A34 = 1.

the solution is confirmed.

the least positive value you can get is 1.

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