# 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 that includes a quadratic term.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Substitute Numerical Values for Formulae/Expressions

Difficulty level:

### 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 = (2×12) − (3×1) + 5 = 4

T2 = (2×22) − (3×2) + 5 = 7

T3 = (2×32) − (3×3) + 5 = 14

T4 = (2×42) − (3×4) + 5 = 25

T5 = (2×52) − (3×5) + 5 = 40

T20 = (2×202) − (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

15
EDDIE SAYS
We are looking for the first term so n = 1. 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

29
EDDIE SAYS
We are looking for the second term so n = 2. 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

49
EDDIE SAYS
We are looking for the third term so n = 3. 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

75
EDDIE SAYS
We are looking for the fourth term so n = 4. 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

107
EDDIE SAYS
We are looking for the fifth term so n = 5. 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

7757
EDDIE SAYS
We are looking for the fiftieth term so n = 50. 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

9
EDDIE SAYS
We are looking for the first term so n = 1. 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

29
EDDIE SAYS
We are looking for the second term so n = 2. 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

59
EDDIE SAYS
We are looking for the third term so n = 3. 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

2099
EDDIE SAYS
We are looking for the twentieth term so n = 20. T20 = (5 × 20²) + (5 × 20) - 1 = (5 × 400) + 100 - 1 = 2000 + 100 - 1 = 2099
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