(i) 7, 13, 19, . . . , 205
(ii) 18, 15 ½ , 13, . . . , – 47
Solution:
(i) 7, 13, 19, . . . , 205
Here,
First term, a = 7
Common difference, d = a2 − a1 = 13 − 7 = 6
Let n be the number of terms in the given AP.
an = 205
We know that,
an = a + (n − 1) d
205 = 7 + (n − 1) 6
198 = (n − 1) 6
33 = (n − 1)
n = 34
Therefore, the given AP has 34 terms in it.
(ii) 18, 15 ½ , 13, . . . , –47
Here,
First term, a = a1 = 18
Common difference, d = a2 − a1 = 15 ½ – 18 = (31/2) – 18 = -5/2
Let n be the number of terms in the given AP.
an = -47
We know that,
an = a + (n − 1) d
-47 = 18 + (n – 1)(-5/2)
-47 – 18 = (n – 1)(-5/2)
-65 × (-2/5) = (n – 1)
26 = n – 1
n = 27
Therefore, the given AP has 27 terms in it.