Sequences - Nth Term

Question 1

Find the first 3 terms of a sequence when Tn= 5n+3

Tip: n = 1

Answer 1

For the 1st term, n=1

👉🏻 T1 = (5X1) + 3
👉🏻 T1 = 5 + 3
👉🏻 T1 = 8

T2 = (5X2) + 3
10 + 3 = 13
T2 = 13

T3 = (5X3) + 3
15 + 3
T3 = 18

Question 2

Generate the first 5 terms in a sequence when Tn = 2n -3

Answer 2

T1 = (2X1) - 3
= 2 - 3 = -1

T2 = (2X2) - 3
= 4 - 3 = 1

T3 = (2X3) - 3
= 6 - 3 = 3

T4 = (2X4) - 3
= 8 - 3 = 5

T5 = (2X5) - 3
= 10 - 3 = 7

Question 3

Generate the first 5 terms of a sequence when Tn = 4n + 5

Answer 3

T1 = (4X1) + 5
= 4 + 5 = 9

T2 = (4X2) + 5
= 8 + 5 = 13

T3 = (4X3) + 5
= 12 + 5 = 17

T4 = (4X4) + 5
= 16 + 5 = 21

T5 = (4X5) + 5
= 20 + 5 = 25

Question 4

If a rule to a sequence is Tn = 26 - 3n, what would be the first 5 terms!

Answer 4

For the first term:
👉🏻T1 = 26 - 3n
👉🏻T1 = 26 - (3X1)
👉🏻T1 = 26 - 3 = 23

👉🏻T1 = 23

T2 = 26 - (3X2)
= 26 - 6 = 20

T3 = 26 - (3X3)
= 26 - 9 = 17

T4 = 26 - (3X4)
= 26 - 12 = 14

T5 = 26 - (3X5)
= 26- 15 = 11

Question 5

If Tn = n2 + 13, what are the first five terms in the sequence?

Answer 5

For the first term:
👉🏻T1 = 1squared + 13
👉🏻T1 = 1 + 13
👉🏻T1 = 14

T2 = 2squared + 13
= 4 +13 = 17

T3 = 3squared +13
= 9 + 13 = 22

T4 = 4squared + 13
= 16 + 13 = 29

T5 = 5squared + 13
= 25 + 13 = 38

Question 6

Term to term rules

Fill in the first 5 terms of the sequence if :

1st term = 3
And the rule is
Add 7

Answer 6

1st   = 3
        \+ 7 
2nd = 10
        \+ 7
3rd  = 17
        \+ 7
4th  = 24
        \+ 7
5th  = 31

Question 7

Term to term rules

Fill in the first 5 terms of the sequence if :

3rd term = 16
And the rule is
Subtract 9

Answer 7

Add 9 to get the second term and another 9 to get the third term then subtract 9 (following the term-to-term rule)

1st   = 34
        - 9
2nd = 25
        - 9
3rd  = 16
        - 9
4th  = 7
        - 9
5th  = - 2

Question 8

Term to term rules

Fill in the first 5 terms of the sequence if :

5th term = 3
And the rule is
Divide by 2

Answer 8

To get the 4th term times 3 by 2:

1st   = 48
        % 2
2nd = 24
        % 2
3rd  = 12
        % 2
4th  = 6
        % 2
5th  = 3

Question 9

Term to term rules

Fill in the first 5 terms of the sequence if :

The 1st term = 5
And the rule is
Multiply by 2 then add 1

Answer 9

1st   = 5
        X 2 + 1
2nd = 11
        X 2 + 1
3rd  = 23
        X 2 + 1
4th  = 47
        X 2 + 1
5th  = 95

Question 10

Term to term rules

Fill in the first 5 terms of the sequence if :

The 2nd term = 2
And the rule is
Multiply by 4 and divide by 2

Answer 10

For the first term divide by 4 and times by 2

1st   = 1 (2%4X2 =1)
        x 4 % 2
2nd = 2
        X 4 % 2
3rd  = 4
        X 4 % 2
4th  = 8
        X 4 % 2
5th  = 16