Exam 7: Sequences; Induction; the Binomial Theorem

Solve the problem. -A theater has 34 rows with 24 seats in the first row, 29 in the second row, 34 in the third row, and so forth. How many seats are in the theater?

An arithmetic sequence is given. Find the common difference and write out the first four terms. - $\left\{ \frac { 1 } { 9 } + \frac { n } { 7 } \right\}$

Solve the problem. -A brick staircase has a total of 16 steps The bottom step requires 117 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?

The sequence is defined recursively. Write the first four terms. -a1 = 2, a2 = 5 and a_n = a_n- 2 - 3a_n- 1 for n ≥ 3

Find the indicated term of the sequence. -The thirteenth term of the arithmetic sequence 28, 24, 20, ...

Evaluate the factorial expression. - $\frac { 10 ! } { 5 ! 5 ! }$

Express the sum using summation notation. - $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

Determine whether the sequence is geometric. -4, 12, 36, 108, 324, ...

Express the sum using summation notation. - $\sum _ { k = 2 } ^ { 5 } ( - 1 ) ^ { k + 1 } ( k - 1 ) ^ { 2 }$

Find the sum of the arithmetic sequence. --3 + 1 + 5 + 9 + 13 + ... + (4n - 7)

Find the indicated term using the given information. --11 , -5 , 1 , ... ; a 27

Evaluate the factorial expression. - $\frac { n ( n + 6 ) ! } { ( n + 7 ) ! }$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 4 } ( k + 4 )$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 2 } { 3 } , \frac { 8 } { 3 } , \frac { 32 } { 3 } , \frac { 128 } { 3 } , \frac { 512 } { 3 }$

Express the sum using summation notation. - $\sum _ { k = 3 } ^ { 5 } \left( k ^ { 2 } - 8 \right)$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 1 } { 9 } , \frac { 1 } { 14 } , \frac { 1 } { 19 } , \frac { 1 } { 24 }$

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -9th term is 74; 13th term is 114

Write out the first five terms of the sequence. -{2n}

Find the indicated term using the given information. - $a = - 8 , d = \frac { 3 } { 4 } ; a_ {49}$

Find the indicated term using the given information. -a = -9 , d = -3 ; a8