Question

In a G.P nth term a = 2n-1, then find common ratio.​

Answer 1

Answer:

2

Step-by-step explanation:

2(1)-1=1

2(2)-1=3

3-1=2

Answer 2

The common ratio (r) of a GP(r) = 2

Step-by-step explanation:

Given,

The nth term of a GP $(a_{n})$ = $2^{n-1}$

Let r be the common ratio of a GP.

To find, the common ratio (d) = ?

Put n = 1, 2, 3, 4, 5, ........

The 1st term of a GP $(a_{1})$ = $2^{1-1}=2^{0} =1$

The 2nd term of a GP $(a_{2})$ = $2^{2-1}=2^{1} =2$

The 3rd term of a GP $(a_{3})$ = $2^{3-1}=2^{2} =4$

The 4th term of a GP $(a_{4})$ = $2^{4-1}=2^{3} =8$

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We know that,

Common ratio (r) = $\dfrac{a_{2}}{a_{1}} =\dfrac{a_{3}}{a_{2}}$

∴ $\dfrac{a_{2}}{a_{1}} =\dfrac{2}{1} =2$

and $\dfrac{a_{3}}{a_{2}} =\dfrac{4}{2} =2$

∴ The common ratio (r) of a GP(r) = 2