Question

The sum of the $4^{th}$ and the $8^{th}$ terms of an A. P . is 24 and the sum of the $6^{th}$ and the ${10}^{th}$ terms of the same A. P. is 34. Find the first three terms of the A. P.

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 = 34 ( given )
a 6 +a 10 = 34
a + 5d +a+ 9d = 34
2a + 14 =34
a + 7d = 17 .....................(ii)
Solving (i) & (ii)
a +7 d = 17
a + 5d = 12
- - -

2d = 5
d = 2.5
From equation (i) ,
a + 5d = 12
a + 5 (2.5) = 12
a+1.2 5= 12
a = 10.75
a 2 = a+d = 10.75+2.5 = 13.25
a 3 = a + 2d = (10.75)+5 = 15.75
10.75,13.25,15.75