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General Form of an AP

Question 9 If...

Question

Question 9
If the $3^{r d}$ and the $9^{t h}$ terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero?

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Solution

$G i v e n t h a t, a_{3} = 4 a_{9} = - 8 W e k n o w t h a t, a_{n} = a + (n - 1) d a_{3} = a + (3 - 1) d 4 = a + 2 d \dots \dots (i) a_{9} = a + (9 - 1) d - 8 = a + 8 d \dots \dots (i i) O n s u b t r a c t i n g e q u a t i o n (i) f r o m (i i), w e g e t, - 12 = 6 d d = - 2 F r o m e q u a t i o n (i), w e g e t, 4 = a + 2 (- 2) 4 = a - 4 a = 8 L e t n^{t h} t e r m o f t h i s A . P . b e z e r o . a_{n} = a + (n - 1) d 0 = 8 + (n - 1) (- 2) 0 = 8 - 2 n + 22 n = 10 n = 5 H e n c e, 5^{t h} t e r m o f t h i s A . P . i s 0.$

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