The given sequence is 5, 10, 15, 20, 25. To find the nth term, we first observe the pattern in the numbers. Each term increases by 5, indicating that this is an arithmetic sequence.
We can express the nth term of an arithmetic sequence using the formula:
a_n = a_1 + (n – 1) * d
Where:
- a_n = nth term
- a_1 = first term (which is 5)
- d = common difference (which is also 5)
- n = term number
Substituting the known values into the formula, we get:
a_n = 5 + (n – 1) * 5
This simplifies to:
a_n = 5 + 5n – 5
Therefore:
a_n = 5n
The answer to the problem is option c) 5n.