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  • 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.​

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.​

Answers (2)

best_answer

Let "a" be the first term and "d" be the common difference.

It is given that - 
a₅ + a₉ = 72 and, a₇ + a₁₂ = 97

( a + 4d ) + ( a + 8d ) = 72

And ( a + 6d ) + ( a + 11d ) = 97

So,

2a + 12d = 72  -- ( 1 )

2a + 17d = 97 --- ( 2 )

Subtracting ( 1 ) from ( 2 )

5d = 25

d = 5

Put this value of d in ( 1 ) we get :-

2a+60 = 72

2a = 12

a=6

So,

a = 6 and d= 5

Hence, the A.P will be 6,11,16,21........

Posted by

Deependra Verma

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a5 + a9 = 72

a + 4d + a + 8d = 72

2a + 17d = 72 ---------(1)

 

a7 + a12 = 97

a + 6d + a + 11d = 97

2a + 17 = 97 ---------(2)

 

By elimination method we get d = 5,,

2a + 12d = 72

2a + 12(5) = 72

2a + 60 = 72

2a = 72 - 60

2a = 12

a = 12/2

a = 6,,

 

So,, we get a = 6 & d = 5 

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

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

6, 11, 16, 21,......

 

               -----------•-----------

Posted by

Aniya

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