Question 5 (ii)
Find the number of terms in each of the following A.P.
(ii) $18, 15 \frac{1}{2}, 13 \dots \dots - 47$

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Solution

(ii)
$F o r t h i s A . P, a = 18 d = a_{2} - a_{1} = 15 \frac{1}{2} - 18 d = \frac{31 - 36}{2} = \frac{- 5}{2} L e t t h e r e a r e n t e r m s i n t h i s A . P . a_{n} = - 47 a_{n} = a + (n - 1) d - 47 = 18 + (n - 1) (\frac{- 5}{2}) - 47 - 18 = (n - 1) (\frac{- 5}{2}) - 65 = (n - 1) (\frac{- 5}{2}) (n - 1) = \frac{- 130}{- 5} (n - 1) = 26 n = 27 T h e r e f o r e, t h i s g i v e n A . P . h a s 27 t e r m s i n i t .$

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