Question

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

Answer 1

Answer:

the sum of 5th , 9th term of an ap is 72 and the sum of 7th and 12th term is 97 find the ap. let a is first term and difference is d

5th term= a+4d, 9th term= a +8d

so, sum = a+4d + a +8d = 2a +12 d = 72

2a +12 d = 72-----(1)

7th= a +6d and 12th = a+11 d

so sum = a +6d + a +11d = 2a +17 d = 97

=>2a +12 d + 5d = 97

=>72 + 5d = 97 (putting value of 2a + 12d from eq 1)

=>5d= 97-72= 25

=>d= 5

put value of d in eq 1

=> 2a +12 d = 72

=> 2a + 12 X 5 =72

=>2a = 72 - 60 =12

=> a =6 and d=5 answer

Answer 2

Answer:

1st

a+4d+a+8d=72

=2a+12d=72

=a+6d=36

2nd

a+6d+a+11d=97

=2a+17d=97

1st 2a+12d=72

2nd 2a+17d=97

- - -

-5d= 25

d=5

1st a+30=36

a=6