Question

1) Find
\[a(4)\] in the sequence 3, 5, 7, ...
\[a(4)=\]

Answer 1

The sequence given is 3, 5, 7, ...

To find the general term of the sequence, we observe that it starts at 3 and increases by 2 with each term. The sequence can be categorized as an arithmetic sequence where:

- The first term \( a(1) = 3 \)
- The common difference \( d = 5 - 3 = 2 \)

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

\[
a(n) = a(1) + (n-1)d
\]

Substituting the values we have:

\[
a(n) = 3 + (n-1) \cdot 2
\]

To find \( a(4) \), we substitute \( n = 4 \) into the formula:

\[
a(4) = 3 + (4-1) \cdot 2
\]

Calculating further:

\[
a(4) = 3 + 3 \cdot 2
\]
\[
a(4) = 3 + 6
\]
\[
a(4) = 9
\]

Thus, the value of \( a(4) \) is:

\[
\boxed{9}
\]