This activity 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
Tn = 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
It might look a bit daunting, but just take it slowly, one step at a time and you'll soon be flying through them!
Let's get started.
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Teacher explanation