  # 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:   #### Worksheet Overview

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

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