# 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):

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