Exam 13: Sequences and Series

The first term of the arithmetic sequence is $\frac { 2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$ Which term of this sequence is $- \frac { 20 } { 3 }$ ?

A city was incorporated in 2004 with a population of 45,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence $P _ { n } = 45000 ( 1.02 ) ^ { n }$ Find the population in 2014

The seventh term of an arithmetic sequence is $- 16$ and the tenth term is $- 31$ ) Find the twenty-fourth term

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$ .

The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic find the common difference. If the sequence is geometric find the common ratio. $- 5 , - 2 s , - 3 s , - 4 s , \ldots$

Determine whether the expression is a partial sum of a arithmetic or geometric sequence. Then find the sum. $2.1 + 2.7 + 3.3 + \ldots + 13.5$

Which term of the arithmetic sequence $\frac { 1 } { 2 } , 2 , \frac { 7 } { 2 } , \ldots$ is $14$ ?

How much money must be invested now at $5 \%$ per year, compounded semi-annually, to fund an annuity of $14$ semi-annual payments of $\$ 100$ each, the first payment being six months after the initial investment?

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term.

Find the first four terms and the $1000 ^ { \text {th } }$ term of the sequence $c _ { n } = ( - 1 ) ^ { n } n ^ { 2 }$

Given that the $50 ^ { \text {th } }$ term of an arithmetic sequence is $259$ and the common difference is $5$ , find the first three terms.

The first term of a geometric sequence is $12$ and the second term is $4$ . Find the fifth term.

Find the coefficient of $- a ^ { 5 } b ^ { 3 }$ in the expansion of $( b - a ) ^ { 8 }$

Given that the $50 ^ { \text {th } }$ term of an arithmetic sequence is $30$ and the $7 ^ { \mathrm { th} }$ term is $44$ , find the first term.

Find the amount of an annuity that consists of $15$ annual payments of $\$ 200$ Each into an account that pays $12 \%$ Interest per year

Given that the $5 ^ { \text {th } }$ term of an arithmetic sequence is $30$ and the $7 ^ { \text {th } }$ term is $44$ , find the first term.

Given that the $50 ^ { \text {th } }$ term of an arithmetic sequence is $259$ and the common difference is $5$ , find the first three terms

Find the $n ^ { \text {ct } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic find the common difference. If the sequence is geometric find the common ratio. $- 5 , - 2 s , - 3 s , - 4 s , K$

Dr. Stevens is considering a 30-year mortgage at 6% interest. She can make payments of $2500 a month. What size loan can she afford?