Question

APAn AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429 . Find AP

Answer 1

HELLO DEAR,



Let the first term and the common difference of the A.P are a and d respectively.


A.P contains 37 terms.

So,

the middle most term is (37+1)/2 th term = 19th term.


, three middle most terms of this A.P.are 18th, 19th and 20th terms.

Given

 a 18 + a 19 + a 20 = 225

=> (a + 17d) + (a + 18d) + (a + 19d) = 225

=> 3(a + 18d) = 225

=> a + 18d = 75

=> a = 75 – 18d … (1)



a 35 + a 36 + a 37 = 429

=> (a + 34d) + (a + 35d) + (a + 36d) = 429

=> 3(a + 35d) = 429

=> (75 – 18d) + 35d = 143

=> 17d = 143 – 75 = 68

=> d = 4

Substituting the value of d in equation (1),



WE GET,




a = 75 – 18 × 4 = 3

the A.P. is 3, 7, 11, 15 …


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

plz refer to this attachment