If 4 times the fourth term of an A.P. is equal to 7 times the 7th term, find its 11th term
Answers
Answer:
0
Step-by-step explanation:
4a+12d=7a+42d
3a+30d=0
3(a+10d)=0
a+10d=0
11th term=0
(if question is like ntimes nth term of ap =t times t the term then find t+n the term then,t+n the term is always 0 just information)
EXPLANATION.
4 times the fourth term of an A.P. is equal to 7 times the 7th terms of an A.P.
As we know that,
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
⇒ 4(T₄) = 7(T₇).
⇒ 4(a + 3d) = 7(a + 6d).
⇒ 4a + 12d = 7a + 42d.
⇒ 12d - 42d = 7a - 4a.
⇒ -30d = 3a.
⇒ -10d = a.
11th terms of an A.P.
⇒ T₁₁ = a + (11 - 1)d.
⇒ T₁₁ = a + 10d.
⇒ T₁₁ = -10d + 10d.
⇒ T₁₁ = 0.
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.