Question

Answer the question with proper step.....

Answer 1

Hello Dear 

Let the first term and the common difference of AP are a and d respectively 

Since the AP contains 37 terms . So, the middle most term is (37+1)/2 th term =  19 th term 

Thus, three middle most terms of this AP are 18th , 19th and 20th terms 

Given a(18) + a(19) + a(20) = 225 

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

3( a + 18 d ) = 225 

a + 18 d = 75 

a = 75 - 18 d ____(1) 

ATGC, 

a(35) + a(36) + a(37) = 429 

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

3( a + 35 d) = 429 

(75 - 18 d ) + 35 d = 143 

17 d = 143 - 75 = 68 

d = 4 

Substituting the value of d in equation (1) , we get 

a = 75 - 18 x 4 = 3 

Thus , the AP is 3, 7 , 11 , 15 ...