if 5 times third term is equal to 3 times the 5th term of an ap then p

1.	if 5 times third term is equal to 3 times the 5th term of an ap then prove that third term is divisible by 3
Answer» we know nth term of an ap is given as _tn= a + (n-1)d divisibility of 3 = sum of digits should be a multiple of 3 or = 0 5 x t₃ = 3 x t₅ 5 (a + 2d) = 3 x (a + 4d) 5a + 10d = 3a + 12d 0 = -2a + 2d a = d ---- i t₃ = a + 2d = a + 2a = 3a which is clearly divisible by 3.

if 5 times third term is equal to 3 times the 5th term of an ap then prove that third term is divisible by 3

Answer»

we know nth term of an ap is given as

_tn= a + (n-1)d

divisibility of 3 = sum of digits should be a multiple of 3 or = 0

5 x t₃ = 3 x t₅

5 (a + 2d) = 3 x (a + 4d)

5a + 10d = 3a + 12d

0 = -2a + 2d

a = d ---- i

t₃ = a + 2d = a + 2a = 3a which is clearly divisible by 3.

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if 5 times third term is equal to 3 times the 5th term of an ap then prove that third term is divisible by 3

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