# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/11) | Q#3

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Question

The ninth term of an arithmetic progression is 22 and the sum of the first 4 terms is 49.

i.       Find the first term of the progression and the common difference.

The nth term of the progression is 46.

ii.       Find the value of n.

Solution

i.

From the given information, we can compile following data for Arithmetic Progression (A.P);

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

So we can write 9th term as;

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

So we can write the expression for the sum of 4 terms in the Arithmetic Progression (A.P) is:

We can simultaneously solve the two equations of 9th term and sum of 4 terms;

We can multiply both sides of the equations of 9th term and by 4;

Subtracting the two equations;

Now we can find the first term from any of the two equations above by substituting

We choose equation of 9th term;

ii.

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

Since the nth term is 46.

From (i) we have;

Substituting these in the expression of the nth term.