Arithmetic Sequences (Chapter 1)

Question 1

What does a recursive function look like?

Answer 1

tn+1=tn+d

Question 2

What does a rule look like?

Answer 2

tn=a+(n-1)d

Question 3

Determine first 5 terms tn=5+3(n-1)

Answer 3

5,8,11,14,17

Question 4

Determine first 5 terms tn=3.3-0.7(n+1)

Answer 4

3.3, 1.2, 0.5, -0.2, -0.9

Question 5

Determine recursive function
-1, 3, 7, 11, 15

Answer 5

tn+1=tn+4

Question 6

Determine recursive function
6.2, 4.3, 2.4, 0.5

Answer 6

tn+1=tn+1.9

Question 7

23. 33. 43
        Make rule for nth

Answer 7

tn=23+(n-1)-10
tn=23+10n-10
tn=13+10n

Question 8

40, 43, 46
Make rule for nth

Answer 8

tn=40+ (n-1)-3
tn=40+3n-3
tn=37+3n

Question 9

What does the general form of arithmetic sequences look like?

Answer 9

tn=t1+(n-1)d

Question 10

The 2nd term of an arithmetic sequence is 13 and the 5th term is 31. What is the 17th term of this sequence?

Answer 10

103

Question 11

The 4th term of an arithmetic sequence is 2 and the 9th term is−33. What is the 26th term of thissequence?

Answer 11

-152

Question 12

Determine the first value of the arithmetic sequence which has a common difference of 6 and a 31stterm of 904

Answer 12

724

Question 13

An arithmetic sequence has a first value of 120 and a common difference of 16. Which term has a value of 712?

Answer 13

38

Question 14

What equation when asked to find which term has the stated value?

Answer 14

n=tn-t1 +1
d

Question 15

An employee starts a new job with a$60 000 salary in thefirst year and the promise of a pay rise of$2500 a year.
a.How much will her salary be in their 6th year?b.How long will it take for her salary to reach$85 000?

Answer 15

a. 72,500
b.11

Question 16

When you are asked for the overall value/number, what is the unknown?

Answer 16

tn

Question 17

When you are asked for the term number (how many years, terms ,etc) what is the unknown?

Answer 17

n

Question 18

3 Formulas to add all terms in a sequence
What determines which one you use?

Answer 18

Sn=n(tn+t1) Choose depending on known values
2 (tn, d)

Sn=n (t1+tn)
2

Sn=n (2t1+ (n-1) d)
2

Question 19

If the sum of the first three terms of an arithmetic sequence is 24, and the common difference is d = 7,
what are the first three terms?

Answer 19

1, 8, 15

Question 20

14. A staircase is designed so that the height of each step increases by 0.8 cm for each step. If the height of
    the first step is 15 cm, what is the total height of the first 17 steps?

Answer 20

363.8cm

Question 21

6. Proceeds from the school fete were $3000 in 2000. In
   2001 the proceeds were $3400 and in 2002 they were
   $3800. If they continued in this pattern:
   a. what were the proceeds from the year 2019 fete?
   b. how much in total would the proceeds from school
   fetes since 2000 have amounted to in the year 2019?

Answer 21

a. $10,600
b.$136,000