Question

In an ap 10 times its 10 th term is equal to 30 times its 30th term find 40 th term

Answer 1

Hey there !!

Given :-

→ 10( a₁₀ ) = 30( a₃₀ ) .

To find :-

→ a₄₀ .

Solution :-

We have,

⇒ 10( a₁₀ ) = 30( a₃₀ ) .

⇒ 10( a + 9d ) = 30 ( a + 29d ) .

⇒ 10a + 90d = 30a + 870d .

⇒ 90d - 870d = 30a - 10a .

⇒ - 780d = 20a .

⇒ 20a = -780d .

⇒ 20a + 780d = 0 .

⇒ 20( a + 39d ) = 0 .

⇒ a + 39d = 0/20 .

⇒ a + 39d = 0 .

⇒ a + ( 40 - 1 )d = 0 .

∴ a₄₀ = 0 .

Hence, 40th term of the AP is 0 .

THANKS.

#BeBrainly .