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nth Term of A.P

The 11th te...

Question

The $11^{t h}$ term and the $21^{s t}$ term of an $A . P$ are $16$ and $29$ respectively, then find the $41^{t h}$ term of that $A . P$ .

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Solution

$a_{11} = 16 a_{21} = 29 a_{11} = a + 10 d = 16 a_{21} = a + 20 d = 29 a p p l y t h e e l l i m i n a t i o n m e t h o d a + 10 d = 16 a + 20 d = 29 c h a n g e t h e s i g n y o u w i l l g a t e t h e v a l u e o f d = \frac{13}{10} p u t t h e v a l u e o f d i n e q u a t i o n (1) a + 10 \times \frac{13}{10} = 16 a + 13 = 16 a = 16 - 13 a = 3 a_{41} = a + 40 d a_{41} = 3 + 40 \times \frac{13}{10} = 3 + 4 \times 13 = 3 + 52 a_{41} = 55 H e n c e t h e 41^{t h} t e r m o f A p i s 55$

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