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1.6.13 Standard formulae for arithmetic series (A-level only)

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Question 38
i.

An arithmetic series is defined by its first term a a\,a and common difference ddd. Prove that the sum of the first n n\,n terms is given by the formula:

Sn=n2[2a+(n−1)d] S_n = \frac{n}{2}[2a + (n-1)d] Sn​=2n​[2a+(n−1)d]
[3]
ii a.

A model for the hourly energy output, EkE_kEk​ (in Joules), of a pulsing laboratory generator during the kkk-th hour is given by:

Ek=7k+3(−1)k E_k = 7k + 3(-1)^k Ek​=7k+3(−1)k

Determine the value of: E12E_{12}E12​

[1]
ii b.

∑k=161Ek\sum_{k=1}^{61} E_k∑k=161​Ek​

[4]

1.6.13 Standard formulae for arithmetic series (A-level only) Questions

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