# 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

Question

The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the  31st 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 12th 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 12th 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 1st term from data obtained.

Now we can find the 31st term.

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