Question

an arithmetic progression has 37 terms the sum of the middle term and the two terms adjacent one on either side to it is 225 if the sum of the las
t 3 terms is 429 . find the first three term's of A.P

Answer 1

Answer:

3 , 7 , 11

Step-by-step explanation:

Let say 1 st term = a

common difference = d

total 37 terms

middle term = (37+1)/2 = 19th term

Adjacent term on either side  18th & 20th term

Sum of 18th , 19th & 20th Term = 225

18th term = a + 17d

19th term = a +18d

20th Term = a +19d

Sum = 3a + 54d = 225

a + 18d = 75   - Eq 1

Last three terms are 37th , 36th & 35th Terms

37th Term = a+36d

36th term = a+35d

35th Term = a +34d

Sum of last 3 terms = 429

3a + 105d = 429

a + 35d = 143   - eq 2

Eq2 - eq2

17d = 68

d = 4

a + 18*4 = 75

a = 3

first three terms of ap

a , a=d , a+2d

3 , 7 , 11