Limit of Sequence

Level pending

If \(n\) is a positive integer and the sequence \(\{a_n\}\) is defined as follows, what is \(\displaystyle \lim_{n \to \infty} a_n\): \[a_1=1 \;\; \textrm{and} \;\; a_{n+1} = \frac{1}{2}a_n + 3 ?\]

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