Question

1)the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44.find first 3 terms.

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