Question

Find a5
for an arithmetic sequence if a1=7
and d=4.

a5=

Answer 1

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

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

where:
- \( a_1 \) is the first term,
- \( d \) is the common difference, and
- \( n \) is the term number.

Given:
- \( a_1 = 7 \)
- \( d = 4 \)
- We need to find \( a_5 \).

Using the formula:

\[
a_5 = a_1 + (5 - 1) \cdot d
\]

Substituting the values we have:

\[
a_5 = 7 + (4) \cdot 4
\]
\[
a_5 = 7 + 16
\]
\[
a_5 = 23
\]

Thus, \( a_5 = 23 \).