Question

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

Answer 1

step by step explanation

Answer 2

The sum of 5th term and 9th term of an AP is 72.

$a_{5}$ + $a_{9}$ = 72

[an = a + (n - 1)d

So,

$a_{5}$ = a + (5 - 1) d

Similarly $a_{9}$ = a + 8d ]

a + 4d + a + 8d = 72

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

And sum of 7th and 12th term is 97.

$a_{7}$ + $a_{12}$ = 97

a + 6d + a + 11d = 97

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

Solve (1) and (2) by elimination.

2a + 17d = 97

2a + 12d = 72 (change the signs)

______________

0a + 05d = 25

______________

5d = 25

d = 5

Put value of d in (1)

2a + 12d = 72

2a + 12(5) = 72

2a + 60 = 72

2a = 72 - 60

2a = 12

a = 6

AP = a, a + d, a +2d...

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

$\textbf{6, 11, 16...}$