Find n if the given value of x is the nth term of the given A.P.1, \(

1.	Find n if the given value of x is the nth term of the given A.P.1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\), …; x = \(\frac{171}{11}\)
Answer» Given A.P. 1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\), \(\frac{171}{11}\) Here, a = 1 d = \(\frac{21}{11}\) – 1 = \(\frac{10}{11}\) Last term (n^th term) = \(\frac{171}{11}\) We know that a_n = a + (n – 1)d ⇒ \(\frac{171}{11}\) = 1 + (n-1)\(\frac{10}{11}\) 171 = 11 + 10n – 10 n = 170/10 n = 17

Find n if the given value of x is the nth term of the given A.P.1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\), …; x = \(\frac{171}{11}\)

Answer»

Given A.P. 1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\), \(\frac{171}{11}\)

Here, a = 1 d = \(\frac{21}{11}\) – 1 = \(\frac{10}{11}\)

Last term (n^th term) = \(\frac{171}{11}\)

We know that a_n = a + (n – 1)d

⇒ \(\frac{171}{11}\) = 1 + (n-1)\(\frac{10}{11}\)

171 = 11 + 10n – 10

n = 170/10

n = 17