PCM 11 Unit 1 Extra Work. Name:______

1) Which of the following represents an arithmetic sequence with a common difference of –4?

A. 8, 4, 2, 1 ... B. 20, 24, 28, 32 .. . C. 32, –8, 2, –0.5 .. . D. 20, 16, 12, 8 ...

16 – 20 = – 4 = 12 – 16 = 8 – 12 = – 4

2) p –1, p + 3, 3p –1, in that order, form an arithmetic sequence. Which of the following is/are true about p?

i)p is even ii)p is odd iii)p is a perfect square

A. 1 only B. 1 and 3 only C. 2 only D. 2 and 3 only

(p + 3) – (p – 1) = (3p – 1) – (p + 3) ------> 4 = 2p – 4 ------> 8 = 2p ; 4 = p

3) Two students are asked to write the first four terms of an arithmetic sequence.

Rob writes the sequence –14,–6, 2, 10 .... d= 8, t15 = 98

Jason writes the sequence 166, 162, 158, 154 ..... d= – 4, t15 = 110

Which statement is true about the fifteenth term of these sequences?

A. t15 is the same in each sequence

B. t15 is smaller in Rob's sequence

C. t15 is smaller in Jason's sequence

D. there is not enough information to answer the question

4) If x + 2, 3x –4, and 7x – 6 are the first three terms of an arithmetic sequence, then the first term of the sequence has a numerical value of

A. –2 B. 0 C. 2 D. 2

(3x –4) – (x + 2) = (7x – 6) – (3x –4) ------> 2x – 6 = 4x – 2 ------> – 4 = 2x ; – 2 = x

5) As part of a fitness program, Melissa walks for 35 minutes on day 1 and increases the walking time by 8 minutes each day. She completes the fitness program on the day she first spends more than 3 hours walking. The program is completed on day __ . 3 h = 180 min

A. 17 B. 18 C. 19 D. 20

t1 = 35, d = 8 , 180 = 35 + ( n – 1) 8 ; 145 = 8 n – 8 ; 153 = 8 n ; 19.125 = n

6) The sum of the first 100 terms of the arithmetic series 3 + 1 + (–1) + (–3) + ...... is

A. –1020 B. –1005 C. –9705 D. –9600

t1 = 3 , d = –2 , S100 = 50( 23 + (99–2) = –9600

Use the following information to answer questions# 7 and # 8.

7)Mary Ann's pay in her first year of work was

A. $49 380 B. $53 367 C. $57 354 D. none of the above

8) The total amount that Mary Ann earned as a statistician was

A. $85 263 B. $673 215 C. $843 741 D. $1 346 430

9) Determine the nth term for the sequence 2, –6, 18, ....

A. tn= –3(2)n – 1 B. tn= 2(–3)n – 1 C. tn= (–6)n – 1 D. tn= 2(3)1– n

10) The first term of a geometric series is 3. The sum of the first two terms of the series is 15 and the sum of the first 3 terms of the series is 63. The common ratio is

A. 3 B. 4 C. 5 D.

11)An expression for the sum of the infinite series is

12) The common difference of the arithmetic sequence defined by is

13) If the 15th and 16th terms of an arithmetic sequence are 99 and 92 respectively, the 5th term is

A. 29 B. 36 C. 162 D. 169

14)The sum of the terms of a sequence is represented by

The general term of the sequence is

15) All the terms in a particular arithmetic sequence are whole numbers. If the first three terms can be represented by 2.x + 10, 4x + 30, and 8x + 60, then the sum of the first four terms of the corresponding series is

A. 30 B. 60 C. 170 D. 340

16) If the sum of an infinite series is 72 and the common ratio is , then the first term is

A. 576 B. 63 C. 9 D.