Question

Is -150 a term of the AP 11, 8, 5, 2,... ?

Answer 1

Given : first term (a) = 11 , common difference (d) = 8 - 11 = -3

Let -150 be the nth term
$a_n$ = a + (n - 1) d

-150 = a+(n-1)d
-150 = 11+(n-1) (-3)
-150 = 11 -3n +3
-150 = 14 - 3n
3n = 150 +14
3n=164
n = 164/3
n = 54.66…..

But n should be an integer.
Hence -150 is not the term of the given AP.