Arthemetic Progression

Question

An AP containing 37 terms. The sum of three middle terms is 225 and the sum of last the term is 429 . Find the value of a and d?

Answer 1

x-d + x + x+d = 225

3x = 225

x = 75 = the middle term = 19th term, last term is 37th term = 75 + 18d is the common difference = 429

d = 429-75)/18 = 354/18 = 19 11/18

a is the 1st term = 75 -18d = 75 -18(354/18) = 75-354 = - 279

if you have 3 terms, the middle term is the 2nd: (3+1)/2, average of 1st and last terms

If you have 37 terms, the middle term is the 18th: (37+1)/2 = 19. there are 18 common differences from 1st to middle and 18 common differences from middle to last.