Question

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

Answer 1

HEYA!!!!

Here is your answer :
____________________________

Given,

3rd term = 5

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

7th term = 9

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

solve 1 & 2

a + 2d = 5
a + 6d = 9
(-) (-) (-)
----------------
-4d = -4

d = 1

substitute d in eq 1

a + 2 ( 1) = 5

a + 2 = 5

a = 5 - 2

a = 3

Therefore, ap = 3,4,5,6.....


HOPE THIS HELPS U. .

Answer 2

Answer:-

$\large\sf{We\:have,}$

$\small\sf{a3=a+(3-1)d=a+2d=5........(1)}$

$\small\sf{a2=a+(7-1)d=a+6d=9........(2)}$

$\large\sf{So,from\:eq(1)and(2)}$

$\small\sf{a=3,d=1}$

$\small\sf{Hence,the\:required\:AP\:is\:3,4,5,6,7,.....}$