Given:
The sequence is 5, 15, 25, ... .
To find:
The explicit formula for the nth term of the given sequence.
Solution:
We have,
5, 15, 25, ...
It is an AP because the difference between two consecutive terms are same.
Here,
First term : a = 5
Common difference : d = 15 - 5 = 10
Now, the explicit formula for the nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
[tex]a_n=5+(n-1)10[/tex]
[tex]a_n=5+10n-10[/tex]
[tex]a_n=10n-5[/tex]
Therefore, the required explicit formula for the given sequence is [tex]a_n=10n-5[/tex].
