Question

AP consists of 37 terms the sum of three middle most terms is 225 and the sum of last three terms is 429 find AP

Answer 1

Since there are 37 terms. So, middle most term = (37 + 1)/2 = 19th term

=> 3 middle most terms are

18th, 19th & 20th

a = first term : d = common difference

T18 = a + 17d

T19 = a + 18d

T20 = a + 19d

=> 3a + 54 d = 225 …….. (1)

Now, last 3 terms..

T35 = a+ 34d

T36 = a + 35d

T37 = a + 36d

=> 3a + 105d = 429 ………….. (2)

Eq (1) - eq(2)

51d = 204

=> d = 4

Hence, 3a + 216 = 225

=> a = 3

So, AP is…

3,7,11,15,19,…………..147