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in Arithmetic Progression by (49.2k points)
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Find n if the given value of x is the nth term of the given A.P.

(i) 25,. 50, 75,100,.......; x = 1000

(ii) - 1, - 3, - 5, - 7,....; x = - 151

(iii) 5\(\frac{1}{2}\), 11, 16\(\frac{1}{2}\), 22,.....; x = 550

(iv)1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\),....., x = \(\frac{171}{11}\)

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(i) 25,. 50, 75,100,.......; x = 1000

a = 25, d = 50 – 25 = 25

Last term, l = 1000

Number of terms,

n = \(\frac{l-a}{d}\) + 1

\(\frac{1000-25}{25}\) + 1 = 40

Hence, the value of n is 40

(ii) -1, - 3, - 5, - 7,....; x = - 151

a = - 1, d = - 2

Last term, l = -151

Number of terms,

n = \(\frac{l-a}{d}\) + 1

\(\frac{151-(-1)}{-2}\) + 1 = 76

Hence, the value of n is 76

(iii)  5\(\frac{1}{2}\), 11, 16\(\frac{1}{2}\), 22,.....; x = 550

a = \(\frac{11}{2}\), d = \(\frac{11}{2}\)

Last term, l = 550

l = a + (n – 1) d

1100 = 11n

n = 100

Hence, number of terms, n = 100

(iv)  1, \(\frac{21}{11}\), \(\frac{31}{11}\), \(\frac{41}{11}\),....., x = \(\frac{171}{11}\)

10n = 170

n = 17

Hence, value of n is 17

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