Question

An A.P 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 the A.P

Answer 1

so the no. of terms, n =37
the three middle most terms are 18 19 and 20..
given that sum of 18th 19th and 20th term is 225
let the terms be a18 a19 and a20.
we know that a18= a+(n-1)d
a18=a+17d [a is tge first term]
similarly a19=a+18d
a20=a+19d.....
so the sum is
a+17d + a+18d + a+19d=225
3a + 54d =225 [this is our first equation]
next consider the second condition
following the same steps we will get the equation
a+34d + a+35d + a+36d=429
3a + 105d = 429 [this is our second equation]
on subtracting the first equation from the second we will get
51d=204
d=204/51
d=4
that is, the common difference is 4
now we have to find the first term a.
we have 3a + 54d=225
on substituting 4 in the plce of d,we get
3a+216=225
3a=225-216
3a=9
a=9/3
a=3
AP:3,7,11,15,19,23,27..........147
hope that this will be helpful......