Which term of the GP 5, 10, 20, 40, ..... is 5120 ?

CONCEPT:

Let us suppose a be the first term and r be the common ratio of a GP. Then the general term of a GP is given by: \({a_n} = a{r^{n\; - \;1}}\)

CALCULATION:

Given: The sequence 5, 10, 20, 40, ..... is a GP.

Here, we have to find which term of the given sequence is 5120.

As we know that, the the general term of a GP is given by: \({a_n} = a{r^{n\; - \;1}}\)

Here, a = 5, r = 2 and let a_n = 5120

⇒ 5120 = (5) ⋅ (2)^{n - 1}

⇒ 2^{(n - 1)} = 1024 = 2¹⁰

⇒ n - 1 = 10

⇒ n = 11

Hence, 5120 is the 11th term of the given sequence.