# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#5

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Question

The rth term of an arithmetic series is (2r – 5).

a.   Write down the first three terms of this series.

b.   State the value of the common difference.

c.   Show that

Solution

a.

We are given that rth term of arithmetic series is represented by;

Therefore, to find any term k we substitute k for r in the given expression.

Hence;

b.

Expression for difference  in Arithmetic Progression (A.P) is:

We have found in (a) that;

Therefore;

c.

We are required to derive the expression for the sum of n terms of arithmetic series for which nth  term is (2r-5).

Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is:

We have found in (a) and (b) that;

Since we do not know the total number of terms in the given arithmetic series, we neither know n  nor  .

Therefore;

Substituting these in the expression for sum of  number of terms in the Arithmetic Progression  (A.P):