Find the 20th term from the last of the AP:3,8,13,...,253.

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G i v e n ser i es i s 3, 8, 13, ...253 Here, f i rs t t er m, a = 3 co mm o n d i ff ere n ce, d = 5 L e t u s f in d t h e t o t a l n u mb er o f t er m s a t f i rs t . u se T_{n} = a + (n - 1) d \Rightarrow 253 = 3 + (n - 1) 5 \Rightarrow 250 = (n - 1) 5 \Rightarrow n - 1 = \frac{250}{5} \Rightarrow n - 1 = 50 ∴ n = 51 so, t h ere a re 51 t er m s in g i v e n ser i es . N o w w e kn o w t ha t m^{t h} t er m f ro m l a s t = l a s t t er m - m^{t h} t er m + 1 so, 20 t h t er m f ro m l a s t = 51 - 20 + 1 = 32 He n ce, 20 t h f or m l a s t = 32 t h t er m f ro m f i rs t u se T_{n} = a + (32 - 1) d = 3 + 31 \times 5 = 3 + 155 = 158 He n ce, 20 t h t er m f or m l a s t = 158.

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Question Text	Find the 20th term from the last of the AP:3,8,13,...,253.
Answer Type	Text solution:1
Upvotes	150