Question

. If 4 times the fourth term of an A.P. is equal to 7 times the 7th term, find its 11th term.
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Answer 1

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.

Answer 2

Answer:

0

Step-by-step explanation:

Question:

If 4 times the fourth term of an A.P. is equal to 7 times the 7th term, find its 11th term.

Given:

• 4 times the fourth term of an A.P. is equal to 7 times the 7th term

To find:

• 11th term

Solution:

According to the question:

4(a+3d) = 7(a+6d)

4a+12d=7a+42d

-3a+12d=42d

-3a-30d = 0

3a + 30d = 0

3(a+10d) = 0

a+10d = 0

$\sf{a_{11}}$ = 0

Hence, the 11th term is 0