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Mathematics

In a G.P., common ratio = 2, first term = 3 and last term = 96.

Statement (1): The number of terms in this G.P. = 96 - 3.

Statement (2): a : arn - 1 = 3 : 96

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

G.P.

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Answer

Given,

First term, a = 3

Common ratio, r = 2

Last term = 96

Using the formula;

⇒ Tn = a.rn - 1

⇒ 3 x 2n - 1 = 96

⇒ 2n - 1 = 963\dfrac{96}{3}

⇒ 2n - 1 = 32

⇒ 2n - 1 = 25

⇒ n - 1 = 5

⇒ n = 5 + 1 = 6

And, according to statement 1, the number of terms in this G.P. = 96 - 3 = 93, which is not correct.

So, statement 1 is false.

⇒aarn−1=first termlast term=396=3:96.\Rightarrow \dfrac{a}{ar^{n - 1}} = \dfrac{\text{first term}}{\text{last term}}\\[1em] = \dfrac{3}{96} = 3 : 96.

So, statement 2 is true.

Hence, option 4 is the correct option.

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