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

1.	Is - 47 a term of the AP 5, 2, –1, –4, –7, ….?
Answer» 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, a_n is n^th term and d is common difference of given AP) Formula Used: a_n = a + (n - 1)d a_n = –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.

Answer»

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, a_n is n^th term and d is common difference of given AP)

Formula Used: a_n = a + (n - 1)d

a_n = –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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