# Write the Terms of a Sequence From a Formula

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:

### QUESTION 1 of 10

In this worksheet, we will work out some of 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 = 50 - 4n2

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

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

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

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

So...

1st term T1 = 50 - 4 × 12 = 50 - 4 × 1 = 50 - 4 =  46

2nd term T2 = 50 - 4 × 22 = 50 - 4 × 4 = 50 - 16 =  34

3rd term T3 = 50 - 4 × 32 = 50 - 4 × 9 = 50 - 36 =  14

4th term T4 = 50 - 4 × 42 = 50 - 4 × 16 = 50 - 64 =  -14

5th term T5 = 50 - 4 × 52 = 50 - 4 × 25 = 50 - 100 =  -50

Now we find the 20th and 100th terms.

T20 = 50 - 4 × 202 = 50 - 4 × 400 = 50 - 1600 =  -1550

T100 = 50 - 4 × 1002 = 50 - 4 × 10000 = 50 - 40000 =  -39950

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

Tn = n2 + 1

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 = n2 - 1

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 = 2n2

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 = 5n2

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 = 2n2 + 3

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 = 5n2 - 10

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 = 3n2 + 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 = 4n2 - 5

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 = 10 - n2

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 - 2n2

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 = n2 + 1

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
EDDIE SAYS
T1 = 12 + 1 = 1 + 1 =  2
T2 = 22 + 1 = 4 + 1 = 5
T3 = 32 + 1 = 9 + 1 = 10
T4 = 42 + 1 = 16 + 1 = 17
T5 = 52 + 1 = 25 + 1 = 26
T20 = 202 + 1 = 400 + 1 = 401
T100 = 1002 + 1 = 10000 + 1 = 10001
• Question 2

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

Tn = n2 - 1

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
EDDIE SAYS
T1 = 12 - 1 = 1 - 1 = 0
T2 = 22 - 1 = 4 - 1 = 3
T3 = 32 - 1 = 9 - 1 = 8
T4 = 42 - 1 = 16 - 1 = 15
T5 = 52 - 1 = 25 - 1 = 24
T20 = 202 - 1 = 400 - 1 = 399
T100 = 1002 - 1 = 10000 - 1 = 9999
• Question 3

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

Tn = 2n2

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
EDDIE SAYS
T1 = 2 × 12 = 2 × 1 = 2
T2 = 2 × 22 = 2 × 4 = 8
T3 = 2 × 32 = 2 × 9 = 18
T4 = 2 × 42 = 2 × 16 = 32
T5 = 2 × 52 = 2 × 25 = 50
T20 = 2 × 202 = 2 × 400 = 800
T100 = 2 × 1002 = 2 × 10000 = 20000
• Question 4

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

Tn = 5n2

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
EDDIE SAYS
T1 = 5 × 12 = 5 × 1 = 5
T2 = 5 × 22 = 5 × 4 = 20
T3 = 5 × 32 = 5 × 9 = 45
T4 = 5 × 42 = 5 × 16 = 80
T5 = 5 × 52 = 5 × 25 = 125
T20 = 5 × 202 = 5 × 400 = 2000
T100 = 5 × 1002 = 5 × 10000 = 50000
• Question 5

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

Tn = 2n2 + 3

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
EDDIE SAYS
T1 = 2 × 12 + 3 = 2 × 1 + 3 = 2 + 3 = 5
T2 = 2 × 22 + 3 = 2 × 4 + 3 = 8 + 3 = 11
T3 = 2 × 32 + 3 = 2 × 9 + 3 = 18 + 3 = 21
T4 = 2 × 42 + 3 = 2 × 16 + 3 = 32 + 3 = 35
T5 = 2 × 52 + 3 = 2 × 25 + 3 = 50 + 3 = 53
T20 = 2 × 202 + 3 = 2 × 400 + 3 = 800 + 3 = 803
T100 = 2 × 1002 + 3 = 2 × 10000 + 3 = 20000 + 3 = 20003
• Question 6

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

Tn = 5n2 - 10

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
EDDIE SAYS
T1 = 5 × 12 - 10 = 5 × 1 - 10 = 5 - 10 = -5
T2 = 5 × 22 - 10 = 5 × 4 - 10 = 20 - 10 = 10
T3 = 5 × 32 - 10 = 5 × 9 - 10 = 45 - 10 = 35
T4 = 5 × 42 - 10 = 5 × 16 - 10 = 80 - 10 = 70
T5 = 5 × 52 - 10 = 5 × 25 - 10 = 125 - 10 = 115
T20 = 5 × 202 - 10 = 5 × 400 - 10 = 2000 - 10 = 1990
T100 = 5 × 1002 - 10 = 5 × 10000 - 10 = 50000 - 10 = 49990
• Question 7

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

Tn = 3n2 + 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
EDDIE SAYS
T1 = 3 × 12 + 2 = 3 × 1 + 2 = 3 + 2 = 5
T2 = 3 × 22 + 2 = 3 × 4 + 2 = 12 + 2 = 14
T3 = 3 × 32 + 2 = 3 × 9 + 2 = 27 + 2 = 29
T4 = 3 × 42 + 2 = 3 × 16 + 2 = 48 + 2 = 50
T5 = 3 × 52 + 2 = 3 × 25 + 2 = 75 + 2 = 77
T20 = 3 × 202 + 2 = 3 × 400 + 2 = 1200 + 2 = 1202
T100 = 3 × 1002 + 2 = 3 × 10000 + 2 = 30000 + 2 = 30002
• Question 8

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

Tn = 4n2 - 5

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
EDDIE SAYS
T1 = 4 × 12 - 5 = 4 × 1 - 5 = 4 - 5 = -1
T2 = 4 × 22 - 5 = 4 × 4 - 5 = 16 - 5 = 11
T3 = 4 × 32 - 5 = 4 × 9 - 5 = 36 - 5 = 31
T4 = 4 × 42 - 5 = 4 × 16 - 5 = 64 - 5 = 59
T5 = 4 × 52 - 5 = 4 × 25 - 5 = 100 - 5 = 95
T20 = 4 × 202 - 5 = 4 × 400 - 5 = 1600 - 5 = 1595
T100 = 4 × 1002 - 5 = 4 × 10000 - 5 = 40000 - 5 = 39995
• Question 9

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

Tn = 10 - n2

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
EDDIE SAYS
T1 = 10 - 12 = 10 - 1 = 9
T2 = 10 - 22 = 10 - 4 = 6
T3 = 10 - 32 = 10 - 9 = 1
T4 = 10 - 42 = 10 - 16 = -6
T5 = 10 - 52 = 10 - 25 = -15
T20 = 10 - 202 = 10 - 400 = -390
T100 = 10 - 1002 = 10 - 10000 = -9990
• Question 10

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

Tn = 100 - 2n2

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
EDDIE SAYS
T1 = 100 - 2 × 12 = 100 - 2 × 1 = 100 - 2 = 98
T2 = 100 - 2 × 22 = 100 - 2 × 4 = 100 - 8 = 92
T3 = 100 - 2 × 32 = 100 - 2 × 9 = 100 - 18 = 82
T4 = 100 - 2 × 42 = 100 - 2 × 16 = 100 - 32 = 68
T5 = 100 - 2 × 52 = 100 - 2 × 25 = 100 - 50 = 50
T20 = 100 - 2 × 202 = 100 - 2 × 400 = 100 - 800 = -700
T100 = 100 - 2 × 1002 = 100 - 2 × 10000 = 100 - 20000 = -19900
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