Question

the sum of 4 and 8 term of an ap is 24 and the sum of 6 and 10 term of an ap is 44find 3 terms of ap

Answer 1

Answer:  A.P = -13, -8, -3

Step-by-step explanation:

Given : A4 + A8 = 24

           A6  + A10 = 44

To find : A1, A2, A3

Solution : A4 + A8 = 24   {given}

              A1 + 3d + A1 +7d = 24

             2(A1) +10d = 24.....................eq-1

               A6 +A10 = 44  {given}

           A1 + 5d  +  A1 + 9d = 44

             2(A1) + 14d = 44......................eq-2

     eq-2  -  eq-1

2(A1) + 14d  -  2(A1) - 10d  = 44-24

4d = 20

d = 5

substituting d value in eq-1

we get,

2(A1) + 10*5 = 24

2(A1) =   - 26

A1  =  -13

Therefore, we now have the first term ( -13 ) and common difference ( 5 ) of A.P

A.P = A1, A1+d, A1+2d

A.P = -13, -13+5, -13+2*5

A.P = -13, -8, -3

these are the first 3 terms of A.P.