A rope of length 4m is cut into 10 sections whose lengths form an arithmetic sequence. The largest resulting part is 3 times larger than the smallest part. Find the size of the smallest part.

Answer 1

let x be length of smallest part

let 3x be length of largest part

sum of arithmetic sequence

s = n/2 (a1 + an)

substituting given sum and expressions for a1 and 2:

4 = 10/2 ( x + 3x)

4/5 = 4x

x = 1/5