Question

Given the sequence find the 25th term
{-1,3,7,11…}
103
99
95
91

Answer 1

To find the 25th term of the sequence \(-1, 3, 7, 11, \ldots\), we first need to identify the pattern.

We can observe the differences between the terms:

- \(3 - (-1) = 4\)
- \(7 - 3 = 4\)
- \(11 - 7 = 4\)

The sequence has a common difference of 4, which indicates it is an arithmetic sequence.

The formula for the \(n\)-th term of an arithmetic sequence can be expressed as:

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

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

In this sequence:
- \(a_1 = -1\)
- \(d = 4\)

Now we can calculate the 25th term (\(a_{25}\)):

\[
a_{25} = -1 + (25-1) \cdot 4
\]
\[
a_{25} = -1 + 24 \cdot 4
\]
\[
a_{25} = -1 + 96
\]
\[
a_{25} = 95
\]

Therefore, the 25th term is \(\boxed{95}\).