Math  /  Algebra

QuestionFind the first six terms of the piecewise sequence: an={n22n+3 if n4n22 if n>4a1=a2=a3=a4=a5=a6=\begin{array}{l} a_{n}=\left\{\begin{array}{ll} \frac{n^{2}}{2 n+3} & \text { if } n \leq 4 \\ n^{2}-2 & \text { if } n>4 \end{array}\right. \\ a_{1}=\square \\ a_{2}=\square \\ a_{3}=\square \\ a_{4}=\square \\ a_{5}=\square \\ a_{6}=\square \end{array}

Studdy Solution
Evaluate the sequence for n=6 n = 6 using the expression n22 n^2 - 2 :
a6=622=362=34 a_6 = 6^2 - 2 = 36 - 2 = 34
The first six terms of the sequence are:
a1=15,a2=47,a3=1,a4=1611,a5=23,a6=34 a_1 = \frac{1}{5}, \, a_2 = \frac{4}{7}, \, a_3 = 1, \, a_4 = \frac{16}{11}, \, a_5 = 23, \, a_6 = 34

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