Sample quiz on recursion formulas
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  1. A recursion formula is given by $t_{n}=t_{n-1}+3,\quad t_{1}=0$. Find $t_{4}$.
    $13$
    $12$
    $9$
    $6$
  2. A recursion formula is given by $t_{n}=-2\times t_{n-1},\quad t_{1}=1$. Find $t_{5}$.
    $16$
    $8$
    $-8$
    $-16$
  3. Find a recursion formula for the sequence $1,3,5,7,9,\cdots$.
    $t_{n}=t_{n+1}+2,\quad t_{1}=1$
    $t_{n}=t_{n-1}+2,\quad t_{1}=1$
    $t_{n}=t_{n-1}-2,\quad t_{1}=1$
    $t_{n}=t_{n-2}-2,\quad t_{1}=1$
  4. Find a recursion formula for the sequence $-1,3,-9,27,-81,\cdots$.
    $t_{n}=-3\times t_{n+1},\quad t_{1}=-1$
    $t_{n}=-3\times t_{n-1},\quad t_{1}=-1$
    $t_{n}=-3\times t_{n-2},\quad t_{1}=-1$
    $t_{n}=-3\times t_{n+2},\quad t_{1}=-1$
  5. A recursive formula is given by $t_{n}=a\times t_{n-1}+b,\quad t_{1}=k$. For what values of $a,b,k$ can the sequence be geometric?
    $a=2,~b=0,~k=0$
    $a=1,~b=0,~k=1$
    $a=2,~b=0,~k=1$
    $a=1,~b=0,~k=0$
  6. For what values of $a,b,k$ can the recursive formula $t_{n}=a\times t_{n-1}+b,\quad t_{1}=k$ yield an arithmetic sequence?
    $a=2,~b=0,~k=1$
    $a=2,~b=0,~k=2$
    $a=1,~b=2,~k=1$
    $a=2,~b=0,~k=3$
  7. Find a recursive formula for the sequence $-2,-5,-8,-11,-14,\cdots$.
    $t_{n}=t_{n+1}-3,\quad t_{1}=-2$
    $t_{n}=t_{n-1}+3,\quad t_{1}=-2$
    $t_{n}=t_{n-2}-3,\quad t_{1}=-2$
    $t_{n}=t_{n-1}-3,\quad t_{1}=-2$
  8. Find a recursive formula for the sequence $16,8,4,2,1,\cdots$.
    $t_{n}=\frac{1}{2}\times t_{n+1},\quad t_{1}=16$
    $t_{n}=2\times t_{n-1},\quad t_{1}=16$
    $t_{n}=\frac{1}{2}+t_{n+1},\quad t_{1}=16$
    $t_{n}=\frac{1}{2}\times t_{n-1},\quad t_{1}=16$
  9. A recursive formula is given by $t_{n}=\Big(t_{n-1}\Big)^2+1,\quad t_{1}=1$. Find $t_{5}$.
    $676$
    $677$
    $36$
    $26$
  10. A recursive formula is given by $t_{n}=t_{n+1}+b,\quad t_{1}=1$. If $t_{6}=51$, find $b$
    $b=\frac{51}{6}$
    $b=9$
    $b=10$
    $b=11$