Question

the sum of 4th and 8th term software ap is 24 and the sum of 6th and 10th terms of the same ap is 44 find the first term

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

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 + 7d

a 6 = a + 5d

a 10 = a + 9d

Sum of 4th and 8th term =  24  (Given)

a 4 + a 8 = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12.................... (i)

Sum of 6th and 10th term = 44  (Given)

a 6 + a 10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 ......................(ii)

Solving (i) and (ii), we get,


From equation (i), we get,

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13

a 2 = a + d = − 13 + 5 = −8

a 3 = a 2 + d = − 8 + 5 = −3