Question

determine the Ap whose 3rd term is 5 and 7th term is 9​

Answer 1

Hii friend,

Third term of an AP = 5

a+2d = 5

a = 5-2d.....(1)

Again,

Seventh term of an AP = 9

a+6d = 9.......(2)

Putting the value of A in equation (2)

a+6d = 9

5-2d +6d = 9

4d = 9-5

4d = 4

D = 4/4

d = 1.

Putting the value of D In equation (1)

a = 5-2d

a = 5-2 × 1 = 5-2 = 3

Therefore,

First term of an AP = 3

Second term = a+d = 3+1 = 4

Third term = a+2d = 3 +2 × 1 = 3+2 = 5

Four term = a+3d = 3 + 3 × 1 = 3+3 = 6

AP = a , a+d , a+2d , a+3d.....

=> 3 , 4 , 5 , 6......

HOPE IT WILL HELP YOU.... :-)

Answer 2

HELLO DEAR FRIEND

Given that

in AP

let the first term be A

common difference be d

3rd term = 5

a + (3 - 1)d = 5

a + 2d = 5 ....(1)

also,

7th term = 9

a + (7 - 1)d = 9

a + 6d = 9 ....(2)

(1) - (2)

a + 2d - (a + 6d) = 5 - 9

a + 2d - a - 6d = -4

-4d = -4

$\large{ d = \frac{ \large{ - 4}}{ \large{ - 4}} }$

$\large \boxed{d = 1}$

now by putting the value of d on (1)

a + 2d = 5

a + 2(1) = 5

a + 2 = 5

a = 5 - 2

$\large \boxed{a = 3}$

now,

AP = a, a + d, a + 2d , a + 3d , a + 4d

3 , 3 + 1, 3 + 2(1) , 3 + 3(1) , 3 + 4(1)

3 , 4 , 5 , 6 , 7

SO,

AP =

$\huge \bf \boxed{ \: \: \boxed{3} \: \: \boxed{4} \: \: \boxed{5} \: \: \boxed{6} \: \: \boxed{7} \: \: }$

THANKS