(A) 2n + 1
(B) 2n + 5
(C) 2n + 6
(D) None of these
🧠 Explanation:
The given sequence is $A_n = 2n - 5$. Here, $n = n + 3$ indicates we are finding the term located three positions after the $n^\text{th}$ term. To determine this, we substitute $n+3$ into the original formula:
$$
A_{n+3} = 2(n+3) - 5
$$
Simplifying, we get:
$$
A_{n+3} = 2n + 6 - 5
$$
$$
A_{n+3} = 2n + 1
$$
This means the term three places after the $n^\text{th}$ term has the value $2n + 1$. Such substitutions are common in arithmetic sequences to find terms at specific positions without listing all terms.
