Find the number of terms in the G-P 6-12- 24 - 1536- 8-10-9-6-

The correct option is C 9 Let 1536 be the n^th term Then, a nbsp;= 6, ar = 12, ar^2=24, ar^n 1=1536. ⇒ r=ar/a=12/6=2 ar^n 1=1536 ⇒ 6× (2)^n 1=1536 ⇒ (2)^n 1= ...

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Standard X

Mathematics

General Term of a GP

Find the numb...

Question

Find the number of terms in the G.P 6,12, 24 ... 1536.

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Solution

The correct option is C
9

Let 1536 be the $n^{th}$ term

Then, $a = 6, a r = 12, a r^{2} = 24, a r^{n - 1} = 1536.$

$\Rightarrow r = \frac{a r}{a} = \frac{12}{6} = 2$

$a r^{n - 1} = 1536$

$\Rightarrow 6 \times (2)^{n - 1} = 1536$

$\Rightarrow (2)^{n - 1} = 256$

$\Rightarrow 2^{n - 1} = 2^{8}$

$\Rightarrow n - 1 = 8$

$\Rightarrow n = 9$

So, the total number of terms in the given G.P is 9.

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Find the number of terms in the G.P 6,12, 24 ... 1536.

The correct option is C 9 Let 1536 be the nth term Then, a=6,ar=12,ar2=24,arn−1=1536. ⇒r=ara=126=2 arn−1=1536 ⇒6×(2)n−1=1536 ⇒(2)n−1=256 ⇒2n−1=28 ⇒n−1=8 ⇒n=9 So, the total number of terms in the given G.P is 9.