# 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 Sn.

c.   Find the largest positive value of Sn.

Solution

a.

We can compile following data from the given information for Arithmetic Progression (A.P) ;  We are required to find 25th 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 21st term of the sequence is zero and all latter terms are (will be)  negative.

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

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