Question

an ap consist of 37 terms.the sum of the three middle most terms is 225 and the sum of the last three terms is 429.find the ap

Answer 1

3 middle most terms are 18 ,19 , 20 .

Given, a + 17d + a + 18d + a+ 19d = 225

3a + 54 d = 225

a + 18d = 75 ...eq(1)

Also given,

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

3a + 105 d = 429

a + 35 d = 143 ....eq(2)


Now equation (2)-(1)

a + 35d = 143

a + 18d = 75

============

17d = 68

d = 4 .

Now substitute in a + 35d = 143 .

a + 140 = 143

a = 3 .


Therefore, The A. P is 3 , 7 , 11 , 15 ......

Answer 2

37 term are there
so middle ter will be=37+1/2=19
three most middle term is 18th,19th,20th
given,(a+17d)+(a+18d)+(a+19d)=225
=>3a+54d=225
=>a+18d=75------(1)
again,a+34d+a+35d+a+36d=429
=>3a+105d=429
=>a+35d=143----(2)
(2)-(1)=>17d=68
=>d=4
(1)=>a=3
so 1st term =3
2nd term=a+d=7
3rd term=a+2d=11

37th term=a+36d=147
so ap is 3,7,11,.......,147