Deck 9: Progressions and the Binomial Theorem

Question 1

Find the 56th term in an arithmetic progression where $\mathrm{a}=3$ and $\mathrm{d}=1.5$ .

A) 85.5
B) 87
C) 79.5
D) 82.5

Answer 1

85.5

Question 2

The first term of an arithmetic progression is 15 and the 50th term is - 107.5. Find the common difference, $\mathrm{d}$ .

A) -3.5
B) -2
C) -2.5
D) -3

Answer 2

-2.5

Question 3

Find the sum of the first 27 terms in an arithmetic progression where the first term is 32 and the 27 th term is - 83 .

A) -824.5
B) -688.5
C) - 1552.5
D) -25.5

Answer 3

-688.5

Question 4

Find the 9th term of the geometric progression $1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$

A) $\frac{1}{2187}$
B) $\frac{1}{19683}$
C) $\frac{1}{6561}$
D) $\frac{1}{59049}$

Question 5

Find the sum of the first ten terms of the geometric progression $2,3,4.5,6.65, \ldots$

A) $\frac{59049}{256}$
B) $\frac{58025}{512}$
C) $\frac{58025}{256}$
D) $\frac{59049}{512}$

Question 6

Find the 7th term of $(x-3) 11$ .

A) $336,798 \mathrm{x}^{5}$
B) $-721,710 x^{6}$
C) $240,570 x 5$
D) - 112, $266 \mathrm{x}^{6}$

Question 7

For the problems below find the nth term of the arithmetic progression.

- $5,8,11, \ldots, n=7$

Question 8

For the problems below find the nth term of the arithmetic progression.

- $2,-1,-4, \ldots, n=8$

Question 9

For the problems below find the nth term of the arithmetic progression.

- $-1,0.5,2, \ldots, \mathrm{n}=17$

Question 10

For the problems below find the nth term of the arithmetic progression.

- $7,4.5,2, \ldots,=19$

Question 11

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $a=3, \ell=23, n=6$

Question 12

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $a=3, \ell=-9, n=7$

Question 13

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $12,7,2, \ldots, n=17$

Question 14

For the problems below find the sum of the first $\mathrm{n}$ terms.

-Carmen is employed at an initial salary of $\$ 32,000$ . If she receives an annual raise of $\$ 1100$ , what is her salary for the eighth year?

Question 15

For the problems below, find the nth term of the geometric progression.

- $4,12,36, \ldots, n=5$

Question 16

For the problems below, find the nth term of the geometric progression.

- $2, \frac{1}{2}, \frac{1}{8}, \ldots, \mathrm{n}=7$

Question 17

For the problems below, find the nth term of the geometric progression.

- $-9,-3,-1, \ldots, n=8$

Question 18

For the problems below, find the nth term of the geometric progression.

- $-5,-10,-20, \ldots, n=10$

Question 19

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $a=3, r=\frac{1}{2}, n=4$

Question 20

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $a=2, r=3, n=6$

Question 21

For the problems below find the sum of the first $\mathrm{n}$ terms.

- $81,27,9, \ldots, n=6$

Question 22

A sugar syrup is being cooled at the rate of $25 \%$ each minute. Find the temperature of the syrup after 6 minutes if the original temperature was $512^{\circ} \mathrm{F}$ . (Hint: The temperature after 1 minute is $384^{\circ} \mathrm{F}$ .)

Question 23

For the problems below, find the sum of the infinite geometric series, if possible.

- $15+3+\frac{3}{5}+\ldots+15\left(\frac{1}{5}\right) \mathrm{n}-1+\ldots$

Question 24

For the problems below, find the sum of the infinite geometric series, if possible.

- $12+2+\frac{1}{3}+\ldots+12\left(\frac{1}{6}\right) \mathrm{n}-1+\ldots$

Question 25

For the problems below, find the sum of the infinite geometric series, if possible.

- $\frac{1}{2}+1+2+\ldots+\frac{1}{2}(2) \mathrm{n}-1+\ldots$

Question 26

For the problems below, expand each binomial using the binomial theorem.

- $(x+4 y)^{4}$

Question 27

For the problems below, expand each binomial using the binomial theorem.

- $(2 \mathrm{x}-5)^{6}$

Question 28

For the problems below, expand each binomial using the binomial theorem.

- $(4 \mathrm{x}-3 \mathrm{y})^{5}$

Question 29

For the problems below, find the indicated term of each binomial expansion.

- $(5 x-2 y)^{7}$ fourth term

Question 30

For the problems below, find the indicated term of each binomial expansion.

- $(3 x-5 y)^{6}$ third term