SOLUTION: From a length of rod 600cm in length, 25 pieces are cut off, each 1 cm longer than the preceding piece. If the rod is exactly used up find the length of the first piece cut off.

Algebra ->  Sequences-and-series -> SOLUTION: From a length of rod 600cm in length, 25 pieces are cut off, each 1 cm longer than the preceding piece. If the rod is exactly used up find the length of the first piece cut off.      Log On


   

Question 908146: From a length of rod 600cm in length, 25 pieces are cut off, each 1 cm longer than the preceding piece. If the rod is exactly used up find the length of the first piece cut off.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Natural Number, n.
p, first term, unknown.

p+(1)+(2)+more
p++1-1)*1+(2-1)*1+more
p+(n-1)*1+more, for n going from 1 to 25

sum%28p%2B%28n-1%29%2Ci=1%2C25%29=600

Using the formula for this arithmetic series,
highlight_green%28n%28p%2B%28p%2B%28n-1%29%29%29%2F2=600%29;
Solve for n.