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Finding Terms of a Sequence from a Formula with a Quadratic Term

In this worksheet, students find terms of a sequence from a T-formula with a quadratic term.

'Finding Terms of a Sequence from a Formula with a Quadratic Term' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Substitute Numerical Values for Formulae/Expressions

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

This worksheet is about finding terms of a sequence from a formula with a quadratic term.

 

To find the first 5 terms and the 20th term of the sequence given by the formula

T= 2n2 − 3n + 5

we simply substitute different values for n.

 

The first term is called T1 , where n = 1.

The second term is called T2 , where n = 2 etc.

The twentieth term is called T20 , where n = 20.

 

Examples

T1 = 2×1 − 3×1 + 5 = 4

T2 = 2×4 − 3×2 + 5 = 7

T3 = 2×9 − 3×3 + 5 = 14

T4 = 2×16 − 3×4 + 5 = 25

T5 = 2×25 − 3×5 + 5 = 40

T20 = 2×400 − 3×20 + 5 = 745

Find the first term (i.e T1) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the second term (i.e T2) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the third term (i.e T3) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the fourth term (i.e T4) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the fifth term (i.e T5) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the fiftieth term (i.e T50) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

Find the first term (i.e T1) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

Find the second term (i.e T2) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

Find the third term (i.e T3) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

Find the twentieth term (i.e T20) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

  • Question 1

Find the first term (i.e T1) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
15
EDDIE SAYS
T1 = 3 × 1² + 5 × 1 + 7 = 3 + 5 + 7 = 15
  • Question 2

Find the second term (i.e T2) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
29
EDDIE SAYS
T2 = 3 × 2² + 5 × 2 + 7 = 3 × 4 + 10 + 7 = 12 + 10 + 7 = 29
  • Question 3

Find the third term (i.e T3) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
49
EDDIE SAYS
T3 = 3 × 3² + 5 × 3 + 7 = 3 × 9 + 15 + 7 = 27 + 15 + 7 = 49
  • Question 4

Find the fourth term (i.e T4) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
75
EDDIE SAYS
T4 = 3 × 4² + 5 × 4 + 7 = 3 × 16 + 20 + 7 = 48 + 20 + 7 = 75
  • Question 5

Find the fifth term (i.e T5) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
107
EDDIE SAYS
T5 = 3 × 5² + 5 × 5 + 7 = 3 × 25 + 25 + 7 = 75 + 25 + 7 = 107
  • Question 6

Find the fiftieth term (i.e T50) of the sequence given by the formula

 

Tn = 3n2 + 5n + 7

CORRECT ANSWER
7757
EDDIE SAYS
T50 = 3 × 50² + 5 × 50 + 7 = 3 × 2500 + 250 + 7 = 7500 + 250 + 7 = 7757
  • Question 7

Find the first term (i.e T1) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

CORRECT ANSWER
9
EDDIE SAYS
T1 = 5 × 1² + 5 × 1 - 1 = 5 × 1 + 5 - 1 = 5 + 5 - 1 = 9
  • Question 8

Find the second term (i.e T2) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

CORRECT ANSWER
29
EDDIE SAYS
T2 = 5 × 2² + 5 × 2 - 1 = 5 × 4 + 10 - 1 = 20 + 10 - 1 = 29
  • Question 9

Find the third term (i.e T3) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

CORRECT ANSWER
59
EDDIE SAYS
T3 = 5 × 3² + 5 × 3 - 1 = 5 × 9 + 15 - 1 = 45 + 15 - 1 = 59
  • Question 10

Find the twentieth term (i.e T20) of the sequence given by the formula

 

Tn = 5n2 + 5n - 1

CORRECT ANSWER
2099
EDDIE SAYS
T20 = 5 × 20² + 5 × 20 - 1 = 5 × 400 + 100 - 1 = 2000 + 100 - 1 = 2099
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