Question

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

Answer 1

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

It is given that -

a₅ + a₉ = 72 and, a₇ + a₠₂ = 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........