Summing an Arithmetic Series (HSC SSCE Mathematics Advanced): Quizzes

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Summing an Arithmetic Series
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What does the notation SnS_n represent in an arithmetic progression?

The sum of the first nn terms

Which formula should you use when you know the first term, last term, and number of terms?

Sn=12n(a+ℓ)S_n = \frac{1}{2}n(a + \ell)

How many terms are in the sum of all integers from 100 to 200 inclusive?

101

In the forward-backward derivation method, what does each pair of terms sum to?

(a+ℓ)(a + \ell)

What eventually happens to SnS_n in an AP with negative common difference?

The sum becomes negative

When should you use the formula Sn=12n(2a+(n−1)d)S_n = \frac{1}{2}n(2a + (n-1)d)?

When you know dd but not ℓ\ell

For the series 100+94+88+82+...100 + 94 + 88 + 82 + ..., what is the common difference dd?

−6-6

To find how many terms are in a series when you know aa, dd, and ℓ\ell, which formula do you use?

Tn=a+(n−1)dT_n = a + (n-1)d

Which formula is simpler to use when you have a choice between both?

Sn=12n(a+ℓ)S_n = \frac{1}{2}n(a + \ell)

In solving AP problems with two conditions, what should you define first?

Variables aa and dd

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