21. Given the sequence $$ \{-1,3,7,11, \ldots\} $$, find $$ a_{25} $$. A. 103 B. 99 C. 95 D. 91

Question

UpStudy AI · Accepted Answer

The sequence is arithmetic because the difference between consecutive terms is constant.

1. Identify the first term $$ a_1 $$ and the common difference $$ d $$:
   $$
   a_1 = -1, \quad d = 3 - (-1) = 4
   $$

2. Use the formula for the $$ n $$th term of an arithmetic sequence:
   $$
   a_n = a_1 + (n-1)d
   $$

3. Substitute $$ n = 25 $$, $$ a_1 = -1 $$, and $$ d = 4 $$:
   $$
   a_{25} = -1 + (25-1) \times 4 = -1 + 24 \times 4 = -1 + 96
   $$

4. Simplify:
   $$
   a_{25} = 95
   $$

Thus, the 25th term of the sequence is $$ 95 $$.
The 25th term $$ a_{25} $$ is 95.

21. Given the sequence \( \{-1,3,7,11, \ldots\} \), find \( a_{25} \). A. 103 B. 99 C. 95 D. 91