how to find first term and common difference

Question

an arithmetic progression has 41 terms the sum of first five terms of this A.P is 35 and the sum of last five terms of the same A.P is 395. Find the common difference and the first term.

Answer 1

a, a+d, a+2d, a+3d, a+4d are the first five terms

a+36d, a+37d, a+38d, a+39d, a+40d are the last five terms

add the first five terms to get 5a+10d which equals 35

5a+10d=35

add the last five terms to get 5a+190d which equals 395

5a+190d=395

5a+10d=35

subtract equations

180d=360

d=2

5a+10*2=35

5a+20=35

5a=15

a=3

the first term is 3 and the common difference is 2

3+5+7+9+11=35 (first 5 terms)

75+77+79+81+83=395  (last 5 terms)