Is - 47 a term of the AP 5, 2, –1, –4, –7, ….?

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.


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