Question

if the 5th term of a.p is 0 , proof that its 38th term is triple of its 18th term

Answer 1

CORRECT QUESTION.

If the 8th term of an A.P. is 0 proof that its 38th term is triple of its 18th term.

EXPLANATION.

5th term of an A.P. = 0.

As we know that,

General term of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₈ = a + (8 - 1)d.

⇒ T₈ = a + 7d.

⇒ a + 7d = 0.

⇒ a = -7d.

38th term.

⇒ T₃₈ = a + (38 - 1)d.

⇒ T₃₈ = a + 37d.

⇒ T₃₈ = -7d + 37d.

⇒ T₃₈ = 30d.

18th term.

⇒ T₁₈ = a + (18 - 1)d.

⇒ T₁₈ = a + 17d.

⇒ T₁₈ = -7d + 17d.

⇒ T₁₈ = 10d.

HENCE PROVED.

                                                                                                                                       

MORE INFORMATION.

Supposition of terms in A.P.

(1) = Three terms as : a - d, a, a + d.

(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.

Answer 2

Answer:

Question :-

If the 5th term of an A.P. is 0 proof that its 38th term is triple of its 18th term.

Answer :-

Explanation :-

5th term of an A.P. = 0.

As we know that,

General term of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₈ = a + (8 - 1)d.

⇒ T₈ = a + 7d.

⇒ a + 7d = 0.

⇒ a = -7d.

38th term.

⇒ T₃₈ = a + (38 - 1)d.

⇒ T₃₈ = a + 37d.

⇒ T₃₈ = -7d + 37d.

⇒ T₃₈ = 30d.

18th term.

⇒ T₁₈ = a + (18 - 1)d.

⇒ T₁₈ = a + 17d.

⇒ T₁₈ = -7d + 17d.

⇒ T₁₈ = 10d.

[HENCE PROVED!]

More information :-

Supposition of terms in A.P.:-

(1) = Three terms as : a - d, a, a + d.

(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.

Step-by-step explanation:

$Hope \: u \: get \: it!$