The nth Term of a Sequence (Leaving Cert Mathematics): Flashcards

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The nth Term of a Sequence
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What is the nth term?

A formula to find any term in a sequence directly

What does TnT_n represent?

The nth term formula

What does nn represent in TnT_n?

The position number of the term

What is the common difference?

Same amount added between consecutive terms

First step to find nth term

Find the common difference

If common difference is dd, nth term starts with?

dndn

General form: Tn=?T_n = ? (with first term aa, diff dd)

dn+(a−d)dn + (a - d)

Alternative nth term formula (first term aa, diff dd)

a+(n−1)da + (n - 1)d

Coefficient of nn in formula should equal?

The common difference

If Tn=4n−3T_n = 4n - 3, what is T1T_1?

11

nth term of sequence 3, 7, 11, 15, ...

4n−14n - 1

General pattern for arithmetic nth term

Tn=dn±constantT_n = dn ± \text{constant}

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