Question

Is 144 a term of the AP: 3,7,11..? justify it ?

Answer 1

In a Given A.P ;
a = 3
d = 7-3 = 4
On the contrary let 144 be the nth term of A.P
Tn = 144
n = ?

Tn = a+(n-1)d
144 = 3+(n-1)4
n-1 = 141/4
n = 35.25+1

n = 36.25

As the value of n is a decimal or number, hence 144 is not the term of given A.P

Answer 2

3,7,1,.... is given Ap

first term = a = 3
common difference = d = a2 - a1 = 7-3 =4
let nth term = 144
a+(n-1)d = 144
3+(n-1)4 = 144
(n-1)4 =144-3
(n-1)4 =141
n-1 = 141/4
n= 141/4 +1
n= (141+4)/4
n= 145/4
therefore
n should not be fraction
144 is not the term in an given AP