Question

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

Answer 1

A5+A9=72
a+4d+a+8d=72
2a+12d=72......(1)

A7+A12=97
a+6d+a+11d=97
2a+17d=97........(2)

(2)-(1)
2a+17d=97
-(2a+12d)=72
5d=25
d=5

put the value of d in eqn (1)

2a+12d=72
2a+12(5)=72
2a+60=72
2a=72-60
2a=12
a=12/2
a=6

a.p.series:-6,11.16,.....

Answer 2

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ARITHMETIC PROGRESSION PROBLEM SOLVING!

TO FIND : THE A.P

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

Given that in the Question ;-

a₅ + a₉ = 72 and, a₇ + a₁₂ = 97

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

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

Then we have,

2a + 12d = 72  -- ( 1 )

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

Subtract ( 1 ) from ( 2 )

5d = 25

d = 5

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

2a+60 = 72

2a = 12

a=6

Therefore, a = 6

and d= 5

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