(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