Question 5 (i)
Find the number of terms in each of the following A.P.
(i) 7, 13, 19, .., 205

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Solution

(i)
$F o r t h i s A . P, a = 7 d = a_{2} - a_{1} = 13 - 7 = 6 A s s u m e t h a t t h e r e a r e n t e r m s i n t h i s A . P . a_{n} = 205 W e k n o w t h a t, a_{n} = a + (n - 1) d T h e r e f o r e, 205 = 7 + (n - 1) 6 198 = (n - 1) 6 33 = (n - 1) n = 34 T h e r e f o r e, t h i s g i v e n A . P h a s 34 t e r m s i n i t .$

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