Question

Find the 11th term of the following geometric sequence.

1,5, 25, 125, 625,

Answer 1

9765625

Step-by-step explanation:

The nth term of a geometric sequence can be calculated using the following

`a_n=a_1r^(n-1)_{}`

Where a1 is the first term and r is the common ratio. The value of a1 is 1 and the value of r can be calculated as the ratio between two consecutive numbers, so

5/1 = 5

25/5 = 5

125/25 = 5

625/125 = 5

Therefore, r = 5 and a1 = 1. Replacing this values, we get:

`\begin{gathered} a_n=1\cdot5^(n-1)^{} \\ a_n=5^(n-1) \end{gathered}`

Finally, we can find the 11th term replacing n by 11, so

`a_(11)=5^(11-1)=5^(10)=9765625`

Therefore, the 11th term of the sequence us 9765625