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