Question

Find a5
for an arithmetic sequence if a1=10
and d=5.

Answer 1

In an arithmetic sequence, the \( n \)-th term can be calculated using the formula:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

Given:
- \( a_1 = 10 \)
- \( d = 5 \)

To find \( a_5 \):

\[
a_5 = a_1 + (5 - 1) \cdot d
\]
\[
a_5 = 10 + 4 \cdot 5
\]
\[
a_5 = 10 + 20
\]
\[
a_5 = 30
\]

Therefore, \( a_5 = 30 \).