Question

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

Answer 1

Answer:

0

Step-by-step explanation:

nth term of ap,

a(n) = a+(n-1)d.

Fourth term of ap,

a(4) = a+(4-1)d = a+3d

Seventh term of ap,

a(7) = a+(7-1)d = a+6d

equating 4* a(4)= 7* a(7),

• 4(a+3d) = 7(a+6d)
• 4a + 12d = 7a + 42d
• 3a = -30d
• a = -10d
• a+10d = 0 --------------- eq.1

The 11th term of ap,

a(11) = a+(11-1)d = a+ 10d = 0 -----[ from eq.1 ]

So, a(11) = 0.

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Answer 2

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.