# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#3

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**Question**

The 12^{th} term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the 31^{st} term.

**Solution**

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

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

Therefore, for 12^{th} term;

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

Therefore for the given case where sum of the first 31 terms is 1023;

From equation obtained through 12^{th} term expression we can find the expression for ;

Substituting this in the above equation obtained through expression of sum of 31 terms;

We can find the 1^{st} term from data obtained.

Now we can find the 31^{st} term.

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

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