Question

the sum of 4th and 8th terms of an ap is 24 and the sum of the 6th 10th terms is 44 find the first three terms of the ap

Answer 1

Let the first term of an A.P = a
and the common difference of the given  A.P = d
As we know that 
a n = a+(n-1) d
a 4 = a +( 4-1) d
a 4 = a+3d
Similarly , 
a 8 = a + 7 d 
a 6  = a + 5 d
a 10 = a+ 9d
Sum of 4 th and 8th terms of an A.P = 24 ( given )
a 4 +a 8 = 24
a + 3d + a + 7d = 24
2a + 10 d = 24
a +5d = 12  .....................(i)
Sum of 6 th and 10 th term  of an A.P = 44 ( given )
a 6 +a 10 = 44
a + 5d +a+ 9d = 44
2a + 14 =44
a + 7d = 22  .....................(ii)
Solving (i) & (ii)
a +7 d  = 22
a + 5d = 12
-   -       -

2d  = 10
d = 5
From equation (i) , 
a + 5d = 12
a + 5 (5) = 12
a+2 5= 12
a = - 13
a 2 = a+d = -13+5 = -8
a 3 = a 2 + d = -8+5 = -3
-13 ,-8,-3

Answer 2

-13,-8,-3..............