Edexcel IGCSE Math A 3.1.HC Sums of Arithmetic Series

Practise using nth-term and sum formulae to find totals, unknown term counts or series parameters.

Exam points

derive a or d from stated terms before applying the arithmetic-series sum formula
substitute Sn and solve the resulting equation for the positive integer n
combine term and sum conditions to solve simultaneous equations for series parameters

[Maximum number: 5]

The first term of an arithmetic series is 10
The 20 th term of the series is 86
The sum of the first N terms of the series is 5194
Work out the value of N
Show your working clearly.

Twentieth term:
$86=10+19d\quad\Rightarrow\quad d=4$
Sum:
$5194=\frac{N}{2}\left(2(10)+(N-1)4\right)$ $5194=\frac{N}{2}(4N+16)$ $N^2+4N-2597=0$ (N-49)(N+53)=0

Final answer:
N=49

M1 for finding d=4. M1 for correct substitution into the sum formula. M1 for a correct quadratic. M1 for solving. A1 cao.

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3.1.HC The sum of the first n terms of an arithmetic series question 1