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Write the Terms of a Sequence From a Formula

In this worksheet, students find the first few terms of a sequence from the given T formulae.

'Write the Terms of a Sequence From a Formula' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet, we will learn how to write the terms of a sequence from a rule known as a T formula.

 

Example

 

Find the first 5 terms in the sequence given by the formula:

Tn = 8 - 4n

where n is the position of the term in the sequence.

Additionally find the 20th term and the 100th terms.

 

Answer

 

We get the first term, T1, by substituting n = 1 in the T formula.

 

We get the first term, T2, by substituting n = 2 in the T formula......etc.....

 

So...

 

1st term T1 = 8 - 4 × 1 = 4
2nd term T2 = 8 - 4 × 2 = 0
3rd term T3 = 8 - 4 × 3 = -4
4th term T4 = 8 - 4 × 4 = -8
5th term T5 = 8 - 4 × 5 = -12

 

Now we find the 20th and 100th terms.

 

T20 = 8 - 4 × 20 = 8 - 80 = -72
T100 = 8 - 4 × 100 = 8 - 400 = -392

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n - 2

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n + 6

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n - 2

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n + 9

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n - 7

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n + 7

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100

Find the first 5 terms in the sequence given by the formula:

 

Tn = 100 - n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

 value
T1
T2
T3
T4
T5
T20
T100
  • Question 1

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 5 × 1 = 5
T2 = 5 × 2 = 10
T3 = 5 × 3 = 15
T4 = 5 × 4 = 20
T5 = 5 × 5 = 25
T20 = 5 × 20 = 100
T100 = 5 × 100 = 500
  • Question 2

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n - 2

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 5 × 1 - 2 = 5 - 2 = 3
T2 = 5 × 2 - 2 = 10 - 2 = 8
T3 = 5 × 3 - 2 = 15 - 2 = 13
T4 = 5 × 4 - 2 = 20 - 2 = 18
T5 = 5 × 5 - 2 = 25 - 2 = 23
T20 = 5 × 20 - 2 = 100 - 2 = 98
T100 = 5 × 100 - 2 = 500 - 2 = 498
  • Question 3

Find the first 5 terms in the sequence given by the formula:

 

Tn = 5n + 6

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 5 × 1 + 6 = 5 + 6 = 11
T2 = 5 × 2 + 6 = 10 + 6 = 16
T3 = 5 × 3 + 6 = 15 + 6 = 21
T4 = 5 × 4 + 6 = 20 + 6 = 26
T5 = 5 × 5 + 6 = 25 + 6 = 31
T20 = 5 × 20 + 6 = 100 + 6 = 106
T100 = 5 × 100 + 6 = 500 + 6 = 506
  • Question 4

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 7 × 1 = 7
T2 = 7 × 2 = 14
T3 = 7 × 3 = 21
T4 = 7 × 4 = 28
T5 = 7 × 5 = 35
T20 = 7 × 20 = 140
T100 = 7 × 100 = 700
  • Question 5

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n - 2

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 7 × 1 - 2 = 7 - 2 = 5
T2 = 7 × 2 - 2 = 14 - 2 = 12
T3 = 7 × 3 - 2 = 21 - 2 = 19
T4 = 7 × 4 - 2 = 28 - 2 = 26
T5 = 7 × 5 - 2 = 35 - 2 = 33
T20 = 7 × 20 - 2 = 140 - 2 = 138
T100 = 7 × 100 - 2 = 700 - 2 = 698
  • Question 6

Find the first 5 terms in the sequence given by the formula:

 

Tn = 7n + 9

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 7 × 1 + 9 = 7 + 9 = 16
T2 = 7 × 2 + 9 = 14 + 9 = 23
T3 = 7 × 3 + 9 = 21 + 9 = 30
T4 = 7 × 4 + 9 = 28 + 9 = 37
T5 = 7 × 5 + 9 = 35 + 9 = 44
T20 = 7 × 20 + 9 = 140 + 9 = 149
T100 = 7 × 100 + 9 = 700 + 9 = 709
  • Question 7

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 4 × 1 = 4
T2 = 4 × 2 = 8
T3 = 4 × 3 = 12
T4 = 4 × 4 = 16
T5 = 4 × 5 = 20
T20 = 4 × 20 = 80
T100 = 4 × 100 = 400
  • Question 8

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n - 7

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 4 × 1 - 7 = 4 - 7 = -3
T2 = 4 × 2 - 7 = 8 - 7 = 1
T3 = 4 × 3 - 7 = 12 - 7 = 5
T4 = 4 × 4 - 7 = 16 - 7 = 9
T5 = 4 × 5 - 7 = 20 - 7 = 13
T20 = 4 × 20 - 7 = 80 - 7 = 73
T100 = 4 × 100 - 7 = 400 - 7 = 393
  • Question 9

Find the first 5 terms in the sequence given by the formula:

 

Tn = 4n + 7

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 4 × 1 + 7 = 4 + 7 = 11
T2 = 4 × 2 + 7 = 8 + 7 = 15
T3 = 4 × 3 + 7 = 12 + 7 = 19
T4 = 4 × 4 + 7 = 16 + 7 = 23
T5 = 4 × 5 + 7 = 20 + 7 = 27
T20 = 4 × 20 + 7 = 80 + 7 = 87
T100 = 4 × 100 + 7 = 400 + 7 = 407
  • Question 10

Find the first 5 terms in the sequence given by the formula:

 

Tn = 100 - n

 

where n is the position of the term in the sequence.

 

Additionally find the 20th term and the 100th term.

CORRECT ANSWER
 value
T1
T2
T3
T4
T5
T20
T100
EDDIE SAYS
T1 = 100 - 1 = 99
T2 = 100 - 2 = 98
T3 = 100 - 3 = 97
T4 = 100 - 4 = 96
T5 = 100 - 5 = 95
T20 = 100 - 20 = 80
T100 = 100 - 100 = 0
---- OR ----

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