# Which of the sequences is being generated by an "Explicit Formula"? a n </msu

Which of the sequences is being generated by an "Explicit Formula"?

${a}_{n}={n}^{2}+3$
${a}_{n}=5n-7$
${a}_{n}=\frac{2}{n+1}$
${a}_{n+2}={a}_{n+1}-3{a}_{n}$
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talhekh
1) ${a}_{n}={n}^{2}+3$
$n=1,{a}_{1}=4$
$n=2,{a}_{2}=7$
$n=3,{a}_{3}=12$
$n=4,{a}_{4}=19$
Thus, we have the sequence $4,7,12,19,...$

2) ${a}_{n}=5n-7$
$n=1,{a}_{1}=-2$
$n=2,{a}_{2}=3$
$n=3,{a}_{3}=8$
Thus, we have the sequence $-2,3,8,...$

uplakanimkk
(3) Given: ${a}_{n}=\frac{2}{n+1}$

Sequence: $1,\frac{2}{3},\frac{1}{2},...$

(4) Given: ${a}_{n+2}={a}_{n+1}-3{a}_{n}$

We can’t find terms from this formula , thus, this isn’t explicit formula