Answer:
[tex]a_n=2\cdot (5)^{n-1}[/tex]
Step-by-step explanation:
We have been given the sequence 2, 10, 50, 250, 1250, …
The first term is 2.
When we multiply this term by 5 then we get the second term which is 10
Similarly, When we multiply second term by 5 then we get the third term which is 50.
So, we can conclude that every time we multiply 5 to any term we'll get the next term.
In other words, we can say that the ratio of two consecutive term of this sequence is equal. And hence the sequence is a geometric sequence with common ratio r = 5
nth term of geometric sequence is given by
[tex]a_n=ar^{n-1}[/tex]
On substituting the known values, we get
[tex]a_n=2\cdot 5^{n-1}[/tex]
Therefore, the explicit formula is given by
[tex]a_n=2\cdot (5)^{n-1}[/tex]
The explicit formula for the given sequence is [tex]\rm a_n = 2\times (5)^{n-1}[/tex] and this can be determined by using the formula of the nth term of the geometric progression.
Given :
Sequence --- 2, 10, 50, 250, 1250, …
The following steps can be used in order to determine the explicit formula for the given sequence:
Step 1 - Write the given sequence.
2, 10, 50, 250, 1250, …
Step 2 - The given sequence is in geometric progression.
Step 3 - The geometric ratio is calculated as:
[tex]\rm r = \dfrac{10}{2}=5[/tex]
Step 4 - The nth term formula in the geometric progression is given below:
[tex]\rm a_n = ar^{n-1}[/tex]
where 'a' is the first term and 'r' is the geometric ratio.
Step 5 - Now, substitute the values of the known terms in the above formula.
[tex]\rm a_n = 2\times (5)^{n-1}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/14320920
