Question

The sum of 4th and 8th term of an ap is 24 and the sum of its 6th and 10th term is 44 find sum of first n term of the ap

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 + 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,
a+7d=22
a+5d=12
________
2d=10

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

 

∴The first three terms of this A.P. are −13, −8, and −3.

Answer 2

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