Question

The sum of 4th and 8th term of A.P. is 24 and sum of 6th and 10th terms is 44. Find A.P...

Answer 1

Answers :

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

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