WebWork Sequences 1) list of #'s 2) graph 3) closed form 4) recursive form

4) Write the first 8 terms of the following sequence: $a_1=3,a_{n+1}=a_n+2$¶

$\{3,5,7,9,11,13,15,17\}$

5) Write the first 8 terms of the following sequence: $a_1=1,a_{n+1}=3a_n$¶

$\{1,3,9,27,81,243,729,2187\}$

6) Give the following sequence in closed form: $1,8,15,22,29,...$¶

$7n+1$

Now give the sequence in recursive form.¶

\(a_{1}=1;a_{n+1}=a_{n}+7\)

7) Give the following sequence in closed form: $1,4,9,16,25,36,...$¶

$a_n=n^2$

Now give the sequence in recursive form.¶

\(a_{1}=1;a_{n+1}=a_{n}+\left(2n+1\right)\)

8) Give the following sequence in closed form: $1,2,6,24,120,720,...$¶

$a_n=n!$

Now give the sequence in recursive form.¶

\(a_{1}=1;a_{n+1}=a_{n}\left(n+1\right)\)

Summing Sequences $\mathrm{\Sigma }$¶

$a_n=2n+1$ (closed form) $a_n:3,5,7,9,11,\dots$ $n:1,2,3,4,5,\dots$ \($\text{Format: }\sum _{n=\text{Start Index}}^{\text{end index}}\text{(closed form)}$\) \($\text{Example: }(5+7+9)=\sum _{n=2}^{4}2n+1$\)

9) Write the following as a sum: \($\sum _{n=1}^{12}n$\)¶

$1+2+3+4+5+6+7+8+9+10+11+12$

Now evaluate the sum.¶

$78$

10) Write the following as a sum: \($\sum _{n=2}^5{n}^2$\)¶

$4+9+16+25$

Now evaluate the sum.¶

$54$

11) Write the following as a sum: \($\sum _{n=3}^6(n+1)(n+2)$\)¶

$20+30+42+56$

Now evaluate the sum.¶

$148$

12) Write the following sum using summation notation: $2+4+6+8+10+12$¶

13) Write the following sum using summation notation: $3+5+7+9$¶

14) Write the following sum using summation notation: $1+16+81$¶

15) Write the following sum using summation notation: $1+5+9+13$¶

Is the following a True property of summation notation? Explain in a sentence, using specific examples. \($\sum _{n=1}^{k}x\ast a_n=c\ast \sum _{n=1}^k{a}_n$\)¶