Question

If seven times the seventh term is equal to 11 times the 11th term ,then which term of given AP is zero ?​

Answer 1

Answer:

The 18th term of this AP is 0.

Step-by-step explanation:

ATQ, 7 times the 7th term, is equal to 11 times the 11th term.

We know that a term of an AP can be expressed as the sum of the preceding term and the common difference, i.e, a₃ = a + 2d where a is the first term, a₂ is the second term and '2d' is the common difference times two.

ATQ,

⇒ 7(a₇) = 11(a₁₁)

⇒ 7(a + 6d) = 11(a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 7a - 11a = 110d - 42d

⇒ -4a = 68d

⇒ 68d + 4a = 0

⇒ 4(17d + a) = 0

⇒ a + 17d = 0

17 can be written as (18 - 1)

⇒ a + (18 - 1)d = 0

We know that a + (n - 1)d = an ,

And the above relation is in the form of a + (n - 1)d = a$\sf _{n}$

Here, an = 0, and "n" stands for the position of the term which is 18.

∴ n = 18

Hence, the 18th term of this AP is 0.

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Additional things to know:

• a → First term.

• d → Common difference.

• an → Value of the term.

• n → Position of the term.

• an = a + (n - 1)d

Answer 2

Step-by-step explanation:

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