Question

find the 59th term of the following arithmetic sequence.
3,7,11,15...

Answer 1

In an arithmetic sequence, each term is found by adding a constant difference to the previous term.

First, let's identify the first term and the common difference of the sequence given:

- The first term \( a = 3 \)
- The common difference \( d = 7 - 3 = 4 \)

The formula for the \( n \)-th term of an arithmetic sequence is given by:

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

To find the 59th term, we substitute \( n = 59 \) into the formula:

\[
a_{59} = 3 + (59 - 1) \cdot 4
\]

Calculating the expression step by step:

1. Calculate \( 59 - 1 = 58 \)
2. Multiply by the common difference: \( 58 \cdot 4 = 232 \)
3. Add the first term: \( 3 + 232 = 235 \)

Thus, the 59th term of the sequence is:

\[
\boxed{235}
\]