Question

The sum of the 5th and 9th terms of an AP is 72 and the sum of 7th and 12th terms is 97. Find the AP.​

Answer 1

Answer:

The A.P is 6,11,16,21,......

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Answer 2

Given :-

The sum of the 5th and 9th terms of an A.P is 72 and the sum of 7th and 12th terms is 97.

To find :-

we have to find the A.P ....

Solution :-

Let the first term of A.P be ' a ' and common difference is 'd'

The sum of a5 and a9 is 72

So, a + 4d + a + 8d =72

2a + 12d = 72.........eq (1)

And also given that :-

The sum of a7 and a12 is 97

So, a + 6d + a + 11d = 97

Therefore 2a + 17d = 97.........eq (2)

Subtract eq (1) from eq (2) , we get

2a + 12 d = 72

2a + 17d = 97. [ here the signs will change ]

-5d = -25

d = -25/ -5

d = 5

Substitute d = 5 in equation, [I prefer eq (1)]

2a + 12(5) = 72

2a + 60 =72

2a = 72-60

2a = 12

a = 12/2

therefore a = 6 and d = 5

We know that the form of A.P is...

a , a + d , a + 2d , a + 3d......

Substitute a = 6 ; d = 5 , we get...

6 ,6 + 5 , 6 + 2(5) , 6 + 3(5),.......

Therefore the A.P is 6 ,11,16,21,...........