Question

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

Answer 1

$a5 + a9 = 72$

$(a + 4d) + (a + 8d) = 72 \\ 2a + 12d = 72 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$a7 + a12 = 97$

$(a + 6d) + (a + 11d) = 97 \\ 2a + 17d = 97 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

*picture1*

d=5

Substituting d=5 in eq.

2a+12d=72

2a+12(5)=72

2a=72-60

2a=12

a=6