To Find: –47 is a term of the AP or not.
Given: The series is 5, 2, –1, –4, –7, ….
a1=5, a2= 2, and d=2–5 = –3 (Let suppose an = –47)
NOTE: n is a natural number.
(Where a=a1 is first term, a2 is second term, an is nth term and d is common difference of given AP)
Formula Used: an = a + (n – 1)d
an = –47 = a + (n – 1)d
–47 = 5 + (n – 1)(–3)
–47–5 = (n – 1)(–3) [subtract 5 on both sides]
52 = (n – 1)(3) [Divide both side by ‘–‘]
17.33 = (n – 1) [Divide both side by 3]
18.33 = n [add 1 on both sides]

As n is not come out to be a natural number, So –47 is not the term of this AP.