Question

An 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

Three middle most terms are 18th ,19th and 20th .
Let a be the first term and d be the common difference
T18 = a+(18-1)d = a+17d
T19= a+(19-1)d = a+18d
T20 = a+(20-1)d= a+19d
Their sum = a+17d+a+18d+a+19d= 3a+54d
3a+54d = 225
Simplifying ,we get a+18d = 75 ..............Eq(1)
T37 = a+36d
T36= a+35d
T35= a+34d
Their sum = a+36d+a+35d+a+a+34d= 3a+105d
3a+105d =429
simplifying ,we get
a+35d = 143................... Eq(2)
Subtracting Equation (1) from Eq(2)
a+35d =143
-a -18d = -75
17d = 68
d = 4
Putting d =4 in equation 1 , a +18(4) = 75
a + 72 = 75
a = 3
AP is 3,7,11,15,19,.............