# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#6

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**Question**

An arithmetic sequence has first term a and common difference d.

The sum of the first 10 terms of the sequence is 162.

**a. **Show that 10a + 45d =162

Given also that the sixth term of the sequence is 17,

**b. **write down a second equation in a and d,

**c. **find the value of a and the value of d.

**Solution**

**a.
**

We are given following data of Arithmetic Series;

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

Therefore;

**b.
**

Expression for the general term in the Arithmetic Progression (A.P) is:

Therefore, for given 6^{th} term we can write equation as;

**c.
**

We have found two equations in terms of a and d in (a).

We can simultaneously solve these two equations.

We can find expression for a from second equation;

Substitute this expression of a in first equation;

Substituting in any of the above two equations yields ‘a’;

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