Question

The sum of 4th and 8th terms of an AP is 24, and sum of 6th and 10th term us 44. Find the first three terms of the AP.

Answer 1

let first term is 'a' & common difference is d
4th term + 8th term = a+3d + a+ 7d = 2a+10d =24

6th term+ 10th term = a+5d+a+9d=2a+14d=44

from above two equations
4d=20
d= 5 & a = -13

thus terms are -13 ,-8,3

Answer 2

Hey there !!  

Answer:  

Given that Sum of 4th term and 8th term of an AP is 24. Also Sum of 6th term and 10th term is 44.  

We must find the first term of the given AP.

 4th term of an AP can be written : a + 3d.   6th term = a + 5d, 8th term = a + 7d, 10th term = a + 9d.

Substituting the values we get,

 => a + 3d + a + 7d = 24.

 => 2a + 10d = 24  ...( 1 )

Similarly,

 => a + 5d + a + 9d = 44.

 => 2a + 14d = 44.  

=> a + 7d = 22.   ...( 2 )

Solving ( 1 ) and ( 2 ), we get,  

a + 7d = 22.

 => a = 22 - 7d   ...( 3 )

Substituting the value of 'a' from ( 3 ) in ( 1 ) we get,

=> 2a + 10d = 24  

=> 2 ( 22 - 7d ) + 10d = 24

=> 44 - 14d + 10d = 24  

=> 44 - 4d = 24  

=> 44 - 24 = 4d  

=> 20 = 4d  

=> d = 20 / 4  

=> d = 5.  

Now substituting value of d in ( 3 ) , we get,  

=> a = 22 - 7d  

=> a = 22 - 7 ( 5 )  

=> a = 22 - 35.  

=> a = -13.  

Hence the first term of the AP is ( -13 ). ​

✔✔ Hence, the first three terms of AP is -13, -8, -3. ✅✅  ________________________________