# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#11

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**Question**

The first term of an arithmetic sequence is 30 and the common difference is –1.5.

**a. **Find the value of the 25th term.

The rth term of the sequence is 0.

**b. **Find the value of r.

The sum of the first n terms of the sequence is S_{n}.

**c. **Find the largest positive value of S_{n}.

**Solution**

**a.
**

We can compile following data from the given information for Arithmetic Progression (A.P) ;

We are required to find 25^{th} term ie .

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

Therefore;

**b.
**

We are given that rth term of the sequence is zero. Therefore;

We are required to find r.

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

Therefore;

**c.
**

We are given that sum of n terms is .

We are required to find largest possible positive sum .

We are given that first term of the sequence is 30 and common difference is -1.5.

We have also found in (b) that 21^{st} term of the sequence is zero and all latter terms are (will be) negative.

Therefore, largest possible positive sum of terms is from 1^{st} to 20^{th }term.

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

Therefore for the given case;

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