Question

The sum of 5th and 9th terms of an AP is 72 and the sum of 7th and 12th term is 97 find the ap

Answer 1

Hey there !

a5 = a + 4d

a7 = a + 6d

a9 = a + 8d

a12 = a + 11d

=> a5 + a9 = 72

=> a + 4d + a + 8d = 72

=> 2a + 12d = 72

=> a + 6d = 36

=> a7 = 36

Also we are given that,

=> a7 + a12 = 97

Substituting a7 as 36 we get,

=> 36 + a12 = 97

=> a12 = 97 - 36

=> a12 = 61

=> a + 11d = 61  => ( 1 )

=> a + 6d = 36 => ( 2 )

Subtracting ( 2 ) from ( 1 ) we get,

=> a + 11d - a - 6d = 61 - 36

=> 5d = 25

=> d = 25 / 5 = 5

Hence, common difference is 5.

=> a + 6d = 36

=> a + 6 ( 5 ) = 36

=> a + 30 = 36

=> a = 36 - 30 = 6

Therefore First term is 6.

Hence AP is 6, 11, 16, 21, .....

Hope my answer helped !