Question

What is the explicit formula for this sequence? 2, 10, 50, 250, 1250, …

Answer 1

This is a geometric sequence with first term 2 and common ratio 5.

an = a1 r^(n-1) IS THE GENERAL FORM SO HERE IT IS:-

an = 2(5)^(n-1)

Answer 2

Answer:

$a_n=2\cdot (5)^{n-1}$

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

$a_n=ar^{n-1}$

On substituting the known values, we get

$a_n=2\cdot 5^{n-1}$

Therefore, the explicit formula is given by

$a_n=2\cdot (5)^{n-1}$