# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#2

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**Question**

The first and second terms of a progression are 4 and 8 respectively. Find the sum of the first 10 terms given that the progression is

** i. **an arithmetic progression

** ii. **a geometric progression.

**Solution**

i.

** **

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

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

So we need to find the sum of first 10 terms of Arithmetic Progression (A.P).

The expression for difference in Arithmetic Progression (A.P) is:

For the given case;

Substituting the given values;

ii.

From the given information, we can compile following data about second Geometric Progression (G.P);

Expression for Common Ratio () in a Geometric Progression (G.P) is;

To find the sum of first 10 terms in Geometric Progression (G.P);

Expression for the sum of number of terms in the Geometric Progression (G.P) when is:

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