Question: Find the number of terms in each of the following APs:
i. 7, 13, 19, ……, 205
ii. 18, 15½, 13, ……, -47
Explanatory Answer
i. 7, 13, 19, ……, 205
a = 7, d = 6, an = 205
an = a + (n – 1) d
205 = 7 + (n - 1) 6
198 = (n - 1) 6
n - 1 = \\frac{198}{6}) = 33
n = 34
This AP has 34 terms
ii. 18, 15 ½, 13, ……, -47
a = 18, d = -2.5, an = -47
an = a + (n - 1) d
-47 = 18 + (n - 1) (-2.5)
-65 = (n - 1) (-2.5)
n - 1 = \\frac{-65}{-2.5}) = 26
n = 27
This AP has 27 terms.