Question

the sum of 5th and 9thterm of Ap 72and the sum of 7th and 12th is 47 find Ap​

Answer 1

Step-by-step explanation:

tn = a + ( n - 1 ) d

t5 = a + ( 5 - 1 ) d

t5 = a+ 4d

Similarly , t9 = a+ 8d

t7 = a + 6d

t12 = a + 11d

According to 1st condition ,

t5 + t9 = 72

a + 4d + a + 8d = 72

2a + 12d = 72 ....... 1st equation

According to 2nd condition ,

t7 + t12 = 47

a + 6d + a + 11d = 47

2a + 17d = 47 ....... 2nd equation

Subracting eq 1 and 2 ,

2a + 12d = 72

( - ) 2a + 17d = 47

_______________________

-5d = 25

d = 25

-5

d = -5

put value od d in eq 1

2a + 12 ( -5 ) = 72

2a - 60 = 72

2a = 72 + 60

a = 130

2

a = 65

therefore , the AP is 65 , 60 , 55 , ......