posted by Watermelon .
Given an arithmetic progression -7,-3,1,..., state three consecutive terms in this progression which sum up to 75.
+ 4 = change from term to term
x-4 + x + x+4 = 75
3 x = 75
x = 25
21, 25, 29
Think about how you can locate these three consecutive terms.
What is the first term, and the common difference?
The sum of an AP for the first n terms is given by
S(n) = (n/2)(2a+(n-1)d)
where a = -7, d = 4
So lets say the 3 consecutive terms are the 14,15 and 16th term.
to get the sum of 75 of these 2 terms, i take
S(16) - S(13)
S(n) - (n-3) = 75
substituting the formula,
(n/2)(2a+(n-1)d) - [(n-3)/2][2a+(n-3-1)d] = 75
solve and find n.